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A box contains 2 white, 3 black and 4 red balls . In how many ways can 3 balls be drawn from the box, if at least one ball is to be included in the draw?
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A box contains 2 white, 3 black and 4 red balls . In how many ways can...
Solution:

Step 1: Find the total number of ways of drawing 3 balls

The total number of ways of drawing 3 balls from a box containing 9 balls is:
C(9,3) = (9!)/(3!6!) = 84
Step 2: Find the number of ways of drawing 3 balls with no restrictions

The number of ways of drawing 3 balls with no restrictions is:
C(2,3) + C(3,3) + C(4,3) = 0 + 1 + 4 = 5
Step 3: Find the number of ways of drawing 3 balls with at least one white ball

The number of ways of drawing 3 balls with at least one white ball is:
C(2,1) * C(7,2) = 2 * 21 = 42
Step 4: Find the number of ways of drawing 3 balls with at least one black ball

The number of ways of drawing 3 balls with at least one black ball is:
C(3,1) * C(6,2) = 3 * 15 = 45
Step 5: Find the number of ways of drawing 3 balls with at least one red ball

The number of ways of drawing 3 balls with at least one red ball is:
C(4,1) * C(5,2) = 4 * 10 = 40
Step 6: Find the number of ways of drawing 3 balls with at least one white ball and one black ball

The number of ways of drawing 3 balls with at least one white ball and one black ball is:
[C(2,1) * C(3,1)] * C(4,1) = 2 * 3 * 4 = 24
Step 7: Find the number of ways of drawing 3 balls with at least one white ball and one red ball

The number of ways of drawing 3 balls with at least one white ball and one red ball is:
[C(2,1) * C(4,1)] * C(3,1) = 2 * 4 * 3 = 24
Step 8: Find the number of ways of drawing 3 balls with at least one black ball and one red ball

The number of ways of drawing 3 balls with at least one black ball and one red ball is:
[C(3,1) * C(4,1)] * C(2,1) = 3 * 4 * 2 = 24
Step 9: Find the number of ways of drawing 3 balls with at least one white ball, one black ball, and one red ball

The number of ways of drawing 3 balls with at least one white ball, one black ball, and one red ball is:
C(2
Community Answer
A box contains 2 white, 3 black and 4 red balls . In how many ways can...
Say 1 black ball is to be included, so 6c2*3c1 = 3*15 = 45

Say 2 black balls are to be included, so 6c1*3c2 = 6*3 = 18

Say 3 black balls are to be included, so 6c0*3c3 = 1

Hence, 46+18 = 64.
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Newton's CradleThe device consists of a row of five metal balls positioned to just barely touch one another suspended from a frame by thin wires. On a small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all. All the balls are, ideally, exactly the same size, weight, mass and density. As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best.When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains motionless. But the last ball on the opposite end of the row is thrown into the air, then swings back to strike the other balls, starting the chain reaction again in reverse. This device illustrates the three main principles of Physics - conservation of energy, conservation of momentum and friction. Everything that moves has momentum equal to its mass multiplied by its velocity. Like energy, momentum is also conserved. Momentum is a vector quantity, when 1st ball hits 2nd ball, it's traveling in a specific direction, let's say east to west. This means that its momentum is also moving east to west. Any change in direction of the motion brings a change in the momentum, which cannot happen without the influence of an outside force. That is why 1st ball doesn't simply bounce off 2nd ball, the momentum carries the energy through all the balls in a westward direction. It is to remember that the law of conservation only works in a closed system, which is free from any external force. The Newton's cradle is not a closed system. When 5th ball swings out away from the rest of the balls, it is affected by the force of gravity, which brings the ball down. But, the horizontal line of balls at rest, functions as a closed system, free from any influence of any force other than gravity. It's here, during the small time between the first ball's impact and the 5th ball swinging out, that momentum is conserved.When the momentum is conserved in Newton’s cradle?

Newton's CradleThe device consists of a row of five metal balls positioned to just barely touch one another suspended from a frame by thin wires. On a small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all. All the balls are, ideally, exactly the same size, weight, mass and density. As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best.When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains motionless. But the last ball on the opposite end of the row is thrown into the air, then swings back to strike the other balls, starting the chain reaction again in reverse. This device illustrates the three main principles of Physics - conservation of energy, conservation of momentum and friction. Everything that moves has momentum equal to its mass multiplied by its velocity. Like energy, momentum is also conserved. Momentum is a vector quantity, when 1st ball hits 2nd ball, it's traveling in a specific direction, let's say east to west. This means that its momentum is also moving east to west. Any change in direction of the motion brings a change in the momentum, which cannot happen without the influence of an outside force. That is why 1st ball doesn't simply bounce off 2nd ball, the momentum carries the energy through all the balls in a westward direction. It is to remember that the law of conservation only works in a closed system, which is free from any external force. The Newton's cradle is not a closed system. When 5th ball swings out away from the rest of the balls, it is affected by the force of gravity, which brings the ball down. But, the horizontal line of balls at rest, functions as a closed system, free from any influence of any force other than gravity. It's here, during the small time between the first ball's impact and the 5th ball swinging out, that momentum is conserved.When the 1st ball at one end of the cradle is pulled away and then released, then

Newton's CradleThe device consists of a row of five metal balls positioned to just barely touch one another suspended from a frame by thin wires. On a small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all. All the balls are, ideally, exactly the same size, weight, mass and density. As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best.When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains motionless. But the last ball on the opposite end of the row is thrown into the air, then swings back to strike the other balls, starting the chain reaction again in reverse. This device illustrates the three main principles of Physics - conservation of energy, conservation of momentum and friction. Everything that moves has momentum equal to its mass multiplied by its velocity. Like energy, momentum is also conserved. Momentum is a vector quantity, when 1st ball hits 2nd ball, it's traveling in a specific direction, let's say east to west. This means that its momentum is also moving east to west. Any change in direction of the motion brings a change in the momentum, which cannot happen without the influence of an outside force. That is why 1st ball doesn't simply bounce off 2nd ball, the momentum carries the energy through all the balls in a westward direction. It is to remember that the law of conservation only works in a closed system, which is free from any external force. The Newton's cradle is not a closed system. When 5th ball swings out away from the rest of the balls, it is affected by the force of gravity, which brings the ball down. But, the horizontal line of balls at rest, functions as a closed system, free from any influence of any force other than gravity. It's here, during the small time between the first ball's impact and the 5th ball swinging out, that momentum is conserved.In Newton’s cradle, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures

Newton's CradleThe device consists of a row of five metal balls positioned to just barely touch one another suspended from a frame by thin wires. On a small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all. All the balls are, ideally, exactly the same size, weight, mass and density. As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best.When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains motionless. But the last ball on the opposite end of the row is thrown into the air, then swings back to strike the other balls, starting the chain reaction again in reverse. This device illustrates the three main principles of Physics - conservation of energy, conservation of momentum and friction. Everything that moves has momentum equal to its mass multiplied by its velocity. Like energy, momentum is also conserved. Momentum is a vector quantity, when 1st ball hits 2nd ball, it's traveling in a specific direction, let's say east to west. This means that its momentum is also moving east to west. Any change in direction of the motion brings a change in the momentum, which cannot happen without the influence of an outside force. That is why 1st ball doesn't simply bounce off 2nd ball, the momentum carries the energy through all the balls in a westward direction. It is to remember that the law of conservation only works in a closed system, which is free from any external force. The Newton's cradle is not a closed system. When 5th ball swings out away from the rest of the balls, it is affected by the force of gravity, which brings the ball down. But, the horizontal line of balls at rest, functions as a closed system, free from any influence of any force other than gravity. It's here, during the small time between the first ball's impact and the 5th ball swinging out, that momentum is conserved.What is a closed system?

Newton's CradleThe device consists of a row of five metal balls positioned to just barely touch one another suspended from a frame by thin wires. On a small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all. All the balls are, ideally, exactly the same size, weight, mass and density. As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best.When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains motionless. But the last ball on the opposite end of the row is thrown into the air, then swings back to strike the other balls, starting the chain reaction again in reverse. This device illustrates the three main principles of Physics - conservation of energy, conservation of momentum and friction. Everything that moves has momentum equal to its mass multiplied by its velocity. Like energy, momentum is also conserved. Momentum is a vector quantity, when 1st ball hits 2nd ball, it's traveling in a specific direction, let's say east to west. This means that its momentum is also moving east to west. Any change in direction of the motion brings a change in the momentum, which cannot happen without the influence of an outside force. That is why 1st ball doesn't simply bounce off 2nd ball, the momentum carries the energy through all the balls in a westward direction. It is to remember that the law of conservation only works in a closed system, which is free from any external force. The Newton's cradle is not a closed system. When 5th ball swings out away from the rest of the balls, it is affected by the force of gravity, which brings the ball down. But, the horizontal line of balls at rest, functions as a closed system, free from any influence of any force other than gravity. It's here, during the small time between the first ball's impact and the 5th ball swinging out, that momentum is conserved.Newton’s cradle illustrates the three main principles of Physics

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A box contains 2 white, 3 black and 4 red balls . In how many ways can 3 balls be drawn from the box, if at least one ball is to be included in the draw?
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A box contains 2 white, 3 black and 4 red balls . In how many ways can 3 balls be drawn from the box, if at least one ball is to be included in the draw? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A box contains 2 white, 3 black and 4 red balls . In how many ways can 3 balls be drawn from the box, if at least one ball is to be included in the draw? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 2 white, 3 black and 4 red balls . In how many ways can 3 balls be drawn from the box, if at least one ball is to be included in the draw?.
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