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In how many ways can a committee consisting of 3 men and 2 women be formed from 7 men and 5 women?
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Verified Answer
The correct answer is:
350
Total no. of Men $=7$ Total no. of women $=5$ Required number of ways $={ }^{7} \mathrm{C}_{3} \times{ }^{5} \mathrm{C}_{2}$
$=\frac{7 !}{3 ! 4 !} \times \frac{5 !}{2 ! 3 !}=\frac{7 \times 6 \times 5}{3 \times 2} \times \frac{5 \times 4}{2}$
$=7 \times 5 \times 10=35 \times 10=350$
$=\frac{7 !}{3 ! 4 !} \times \frac{5 !}{2 ! 3 !}=\frac{7 \times 6 \times 5}{3 \times 2} \times \frac{5 \times 4}{2}$
$=7 \times 5 \times 10=35 \times 10=350$
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