Question

A group consist of 10 Democrats and 14 Republicans. How many ways are there of making a committee of a) 7 people? b) 5 Democrats and 2 Republicans? c) 7 Democrats. d) How many committees can you form if three people, Ann, Bob, and Carol, will not serve together?

Answer 1

Given 10 Democrats and 14 Republicans a) committee of 7 people No. of different ways to selecting 7 out of 24 people 24C7 - - 346104 ways // 6) committee of 5 Deusavats and a Republicans 22932 ways // No. of ways (10 CG) (1462) c) committee of 7 Deusocrats No. of ways = 1027 = 120 ways d) 3 people Ann, Bob and carol will not serve together For Ann: No. of ways = Total people 24-2 = 22 (Bob, Card) Let committee size:3 No. of ways = 226; 1540 ways people as it is not Similarly sol Bob and carol also 1540 & 1560 mentioned] ways. Total ways = 3x1540 = 4620 ways // [