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There are 3 boxes and 6 balls. In how many ways these balls can be distributed if all the balls and all the boxes are different?
- a)243
- b)512
- c)729
- d)416
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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There are 3 boxes and 6 balls. In how many ways these balls can be dis...
Answer – C.729 Explanation : 3^6 = 729
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There are 3 boxes and 6 balls. In how many ways these balls can be dis...
Solution:
To distribute the 6 balls into 3 boxes, we have 3 choices for each ball. So, the total number of ways to distribute the balls is $3^6$ since each of the 6 balls has 3 choices of boxes to go into. Therefore, the answer is 729 which is option (c).
Explanation in detail:
We can break down the problem into 6 smaller sub-problems, where we consider each ball separately and determine the number of ways it can be distributed among the 3 boxes.
Consider the first ball. It can be placed in any one of the 3 boxes. Therefore, there are 3 ways to distribute the first ball.
Now, consider the second ball. It can also be placed in any one of the 3 boxes. Therefore, there are 3 ways to distribute the second ball.
Using similar reasoning, we can see that there are 3 ways to distribute the third ball, 3 ways to distribute the fourth ball, 3 ways to distribute the fifth ball, and 3 ways to distribute the sixth ball.
Therefore, the total number of ways to distribute all 6 balls is the product of the number of ways to distribute each ball. That is,
Total number of ways = 3 × 3 × 3 × 3 × 3 × 3 = 3^6 = 729
Therefore, the correct answer is option (c).
To distribute the 6 balls into 3 boxes, we have 3 choices for each ball. So, the total number of ways to distribute the balls is $3^6$ since each of the 6 balls has 3 choices of boxes to go into. Therefore, the answer is 729 which is option (c).
Explanation in detail:
We can break down the problem into 6 smaller sub-problems, where we consider each ball separately and determine the number of ways it can be distributed among the 3 boxes.
Consider the first ball. It can be placed in any one of the 3 boxes. Therefore, there are 3 ways to distribute the first ball.
Now, consider the second ball. It can also be placed in any one of the 3 boxes. Therefore, there are 3 ways to distribute the second ball.
Using similar reasoning, we can see that there are 3 ways to distribute the third ball, 3 ways to distribute the fourth ball, 3 ways to distribute the fifth ball, and 3 ways to distribute the sixth ball.
Therefore, the total number of ways to distribute all 6 balls is the product of the number of ways to distribute each ball. That is,
Total number of ways = 3 × 3 × 3 × 3 × 3 × 3 = 3^6 = 729
Therefore, the correct answer is option (c).
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There are 3 boxes and 6 balls. In how many ways these balls can be dis...
3^6 =729
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