In how many ways can a group of 5 men and 2 women be made out of total of 7 men and 3 women?
Correct Answer: Description for Correct answer:
There are 7 men and 3 women.
We have to select 5 men out of 7 and 2 women out of 3.
This can be done in \( \Large ^{7}C_{5} \times ^{3}C_{2} \) ways.
The number of ways of making the selection
= \( \Large ^{7}C_{5} \times ^{3}C_{2} \)
= \( \Large ^{7}C_{2} \times ^{3}C_{2} \)
\( \Large \left[ Because,\ ^{n}C_{r}=^{n}C_{n-r} \right] \)
= \( \Large \frac{7 \times 6}{1 \times 2} \times \frac{3 \times 2}{1 \times 2} \) = 63
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