Question
Asked Feb 20, 2019
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From a group of 5 men and 7 women a committee of four is to be randomly selected.
Same is one of the men and Ann is one of the women, no committee containing both of them can function. What is the probability that they do not serve ttogether on the same committee?

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Expert Answer

Step 1

Total number of people are 5+7=12

So the total number of ways of selecting 4 people out of 12 is given by 12P4 i.e:

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Step 2

When both Same and Ann  are on the same committee, the number of 4 member committees that can be formed is calculated by selecting 2 members out of the remaining 10 people.

Hence the number of ways committees can be formed having Same and Ann are 10C2 i.e.

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Step 3

Hence, the number of committees that can be formed without having Same and Ann together are given by: 11880-...

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Probability

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