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A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is?
- a)54/199
- b)52/195
- c)53/186
- d)51/126
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A committee of five persons is to be chosen from a group of 10 people....
Five persons is to be chosen from a group of 10 people = 10C5 = 252
Couple Serve together = 8C3 * 2C2 = 56
Couple does not serve = 8C5 = 56
Probability = 102/252 = 51/126
Couple Serve together = 8C3 * 2C2 = 56
Couple does not serve = 8C5 = 56
Probability = 102/252 = 51/126
Most Upvoted Answer
A committee of five persons is to be chosen from a group of 10 people....
Five persons is to be chosen from a group of 10 people = 10C5 = 252
Couple Serve together = 8C3 * 2C2 = 56
Couple does not serve = 8C5 = 56
Probability = (56+56)/252=112/252 = 56/126=28/63
so answer is none of these
Couple Serve together = 8C3 * 2C2 = 56
Couple does not serve = 8C5 = 56
Probability = (56+56)/252=112/252 = 56/126=28/63
so answer is none of these
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A committee of five persons is to be chosen from a group of 10 people....
Problem: A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is?
Solution:
Total possible ways to choose a committee of five persons from 10 people = C(10,5) = 252
Let's consider that the married couple is a single entity, then the total number of entities will be 9.
Now, we can form a committee of 5 people from these 9 entities in C(9,5) = 126 ways.
Out of these 126 ways, the married couple can serve together in C(1,1) * C(8,4) = 70 ways.
The married couple can also choose not to serve together in C(2,1) * C(8,4) = 160 ways.
Therefore, the probability that the married couple will either serve together or not at all is:
P = (70 + 126) / 252 = 196 / 252 = 7 / 9
Thus, the correct option is (D) 51/126.
Solution:
Total possible ways to choose a committee of five persons from 10 people = C(10,5) = 252
Let's consider that the married couple is a single entity, then the total number of entities will be 9.
Now, we can form a committee of 5 people from these 9 entities in C(9,5) = 126 ways.
Out of these 126 ways, the married couple can serve together in C(1,1) * C(8,4) = 70 ways.
The married couple can also choose not to serve together in C(2,1) * C(8,4) = 160 ways.
Therefore, the probability that the married couple will either serve together or not at all is:
P = (70 + 126) / 252 = 196 / 252 = 7 / 9
Thus, the correct option is (D) 51/126.
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A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is?a)54/199b)52/195c)53/186d)51/126e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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