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A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at random. What is the probability that all the balls are of same colour?
- a)33/455
- b)34/455
- c)44/455
- d)47/455
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at ...
(4c3 + 5c3 + 6c3)/15c3 = 34/455
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A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at ...
Problem:
A box contains 4 red, 5 black, and 6 green balls. Three balls are drawn at random. What is the probability that all the balls are of the same color?
Solution:
To find the probability of drawing three balls of the same color, we need to consider each color separately.
Red balls:
There are 4 red balls in the box. We need to choose 3 out of these 4 balls. The number of ways to do this is given by the combination formula: C(4, 3) = 4! / (3! * (4 - 3)!) = 4.
Black balls:
Similarly, there are 5 black balls in the box. We need to choose 3 out of these 5 balls. The number of ways to do this is given by the combination formula: C(5, 3) = 5! / (3! * (5 - 3)!) = 10.
Green balls:
There are 6 green balls in the box. We need to choose 3 out of these 6 balls. The number of ways to do this is given by the combination formula: C(6, 3) = 6! / (3! * (6 - 3)!) = 20.
Total number of ways:
The total number of ways to choose 3 balls out of the 15 balls in the box is given by the combination formula: C(15, 3) = 15! / (3! * (15 - 3)!) = 455.
Probability:
The probability of drawing 3 balls of the same color is the sum of the probabilities for each color. So, the probability is (4 + 10 + 20) / 455 = 34/455.
Therefore, the correct answer is option B) 34/455.
A box contains 4 red, 5 black, and 6 green balls. Three balls are drawn at random. What is the probability that all the balls are of the same color?
Solution:
To find the probability of drawing three balls of the same color, we need to consider each color separately.
Red balls:
There are 4 red balls in the box. We need to choose 3 out of these 4 balls. The number of ways to do this is given by the combination formula: C(4, 3) = 4! / (3! * (4 - 3)!) = 4.
Black balls:
Similarly, there are 5 black balls in the box. We need to choose 3 out of these 5 balls. The number of ways to do this is given by the combination formula: C(5, 3) = 5! / (3! * (5 - 3)!) = 10.
Green balls:
There are 6 green balls in the box. We need to choose 3 out of these 6 balls. The number of ways to do this is given by the combination formula: C(6, 3) = 6! / (3! * (6 - 3)!) = 20.
Total number of ways:
The total number of ways to choose 3 balls out of the 15 balls in the box is given by the combination formula: C(15, 3) = 15! / (3! * (15 - 3)!) = 455.
Probability:
The probability of drawing 3 balls of the same color is the sum of the probabilities for each color. So, the probability is (4 + 10 + 20) / 455 = 34/455.
Therefore, the correct answer is option B) 34/455.
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