Question

From a group of 7 men and 5 women, determine how many committees of 4 people can be formed with: a) no restrictions b) exactly three women c) exactly four men d) no women

Answer 1

Committees can be formed in several ways: with no restrictions, exactly 3 women can form 70 committees, exactly 4 men can form 35 committees, and no women also result in 35 committees of all men.

Step-by-step explanation:

From a group of 7 men and 5 women, multiple scenarios for forming a committee of 4 people can be explored:

• No restrictions: The number of possible committees of 4 people from a total of 12 (7 men + 5 women) can be calculated using combinations: C(12, 4) = 495.
• Exactly three women: Choosing 3 women out of 5 and 1 man out of 7 gives C(5, 3) * C(7, 1) = 10 * 7 = 70 possible committees.
• Exactly four men: Selecting all 4 members from the men gives C(7, 4) = 35 possible committees.
• No women: This is the same scenario as 'exactly four men' because a committee with no women means all men, which is 35 possible committees.