In how many ways u can form a group of 11 members from 5 men and 11 women if…

Method: Choose k men (k = 0 to 3) and the rest women so that the group has 11 members.

Total ways = sum over k = 0 to 3 of C(5,k) × C(11,11 − k).

• k = 0: choose 0 men and 11 women → C(5,0) × C(11,11) = 1 × 1 = 1

• k = 1: choose 1 man and 10 women → C(5,1) × C(11,10) = 5 × 11 = 55

• k = 2: choose 2 men and 9 women → C(5,2) × C(11,9) = 10 × 55 = 550

• k = 3: choose 3 men and 8 women → C(5,3) × C(11,8) = 10 × 165 = 1650

Adding the terms gives:

1 + 55 + 550 + 1650 = 2256