The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is

Step-by-step solution

Since, there are 8 women and 10 men in a group. So, the total number of ways of a committee of 8 member such that committee contains at most 5 men and at least 5 women aligned & = ^8 C ₅ ¹⁰ C ₃+ ^8 C ₆ ¹⁰ C ₂+ ^8 C ₇ ¹⁰ C ₁+ ^8 C ₈ ¹⁰ C ₀ & = 8 7 6 6 10 9 8 6 + 8 7 2 10 9 2 +8 10+1 1 & =6720+1260+81=8061 aligned