In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? Correct Answer 11760

$$\eqalign{ & {\text{Required}}\,{\text{number}}\,{\text{of}}\,{\text{ways}} \cr & = {{}^8{C_5} \times {}^{10}{C_6}} \cr & = {{}^8{C_3} \times {}^{10}{C_4}} \cr & = {\frac{{8 \times 7 \times 6}}{{3 \times 2 \times 1}} \times \frac{{10 \times 9 \times 8 \times 7}}{{4 \times 3 \times 2 \times 1}}} \cr & = 11760 \cr} $$
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