In how many ways 8 members can be selected for a team such that women…
2024
In how many ways 8 members can be selected for a team such that women constitute at least 50% of the team from a group of 8 men and 8 women.
- A.
8C4*8C4+8C5x8C3+8C6x8C2+8C7x8C1+8C8
- B.
8^4*8^4
- C.
8C4x8C4
- D.
8^4x8^4+8^3x8^5+8^2x846+8^7x8+1
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Answer: Total number of ways = 8885
Reason: Women must form at least 50% of an 8-member team, so consider teams with 4, 5, 6, 7, or 8 women. For each case choose the women from the 8 women and the men from the 8 men.
4 women and 4 men: 8C4 × 8C4 = 70 × 70 = 4900
5 women and 3 men: 8C5 × 8C3 = 56 × 56 = 3136
6 women and 2 men: 8C6 × 8C2 = 28 × 28 = 784
7 women and 1 man: 8C7 × 8C1 = 8 × 8 = 64
8 women and 0 men: 8C8 = 1
Hence total = 4900 + 3136 + 784 + 64 + 1 = 8885.