Probability without replacement in forming a committee

Question

In order to pick members for forming a committee, 4 names are randomly drawn from a jar (one by one, without replacement) containing the names of 10 experts. Of the 10 experts, there is one individual, say A, who can play an important role in the committee. What is the probability that individual A will not get picked for the committee role?

a. $0.1$
b. $0.3$
c. $0.4$
d. $0.6$

Here, out of 10 people, the probability of selection without a replacement is equal to ${10 \choose 1}$${9\choose 1}$${8\choose 1}$${7 \choose 1}$. How do I approach after that? Can anyone explain how to solve this question?

Answer 1

Since you are new, and have made some sort of effort, please learn a few things

• choosing without replacement $\equiv$ hypergeometric distribution
• whether you choose one by one or all together, it's the same.
• when you talk of choosing order doesn't matter, so just use $^nC_r$

Hint

Now total possible choices are obviously $^{10}C_4$, and this will form the denominator. Now suppose you are the "special" person and you aren't chosen. What should be the numerator ?

The numerator should be $^9C_4$, shouldn't it ?

But in such a simple case, an easier way exists

Since $4$ out of $10$ are chosen, the probability that any particular person is not chosen is simply $\frac{6}{10}$