Use the specific term of the binomial expansion of (m+w)^(10) when the exponent of w is 7.
15/128
Practice makes perfect
When there are two possible designations for a group, we can use binomial expansion to find probability. Let's let m represent the men and w represent the women. Since there are ten people on the committee, we can use (m+w)^(10).
(m+w)^(10) = ∑_(k=0)^(10)10!/k!(10-k)!m^(10-k)w^kWe need the term when the exponent of w is 7 because we need to know when there are 7 women on the committee. Let's look at the term of the summation when k=7 and evaluate it.
Therefore, the probability that 7 members will be women is 15128.
Alternative Solution
Alternative Interpretation
Sometimes, when working with math, the exercises are not well defined. Since the following phrase is not preceded by an exactly or an at least and because it does not specify the number of men, it could take on multiple meanings. 7of the committee will be women
Other than the previous interpretation and answer, it is possible to have 7, 8, 9, or 10 of the committee be women and still say there are 7 women on the committee. To find the probability we can use the terms of the binomial from where we started above to the end.
