From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is :

Step-by-step solution

Total number of ways = C 1 5 × C 3 10 + C 2 5 × C 2 10 + C 3 5 × C 1 10 + C 4 5 = 5 ! 4 ! × 10 ! 7 ! 3 ! + 5 ! 2 ! 3 ! × 10 ! 8 ! 2 ! + 5 ! 3 ! 2 ! × 10 ! 9 ! + 5 ! 4 ! = 5 × 10 × 9 × 8 3 × 2 + 5 × 4 2 × 1 × 10 × 9 2 + 5 × 4 2 × 1 × 10 + 5 = 5 × 5 × 3 × 8 + 5 × 2 × 5 × 9 + 10 × 10 + 5 = 600 + 450 + 100 + 5 = 1155 Total no. of ways = 1155 No. of ways to form a committee having more women than men =