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Formation of Committees: Women and Men Selection

Learn how to form committees by selecting three women from a group of 20 and four men from a group of 30 without considering the order. Utilize combination formulas for efficient counting.

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Formation of Committees: Women and Men Selection

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  1. 3.2 Combinations

  2. Combinations Counting where order doesn’t matter. Combination Formula: nCr = n!/r!(n-r)! Example: We have a deck of cards and we want 5 cards. They can be any cards. There are 52 cards to a deck. 52C5 52!/5!(52-5)! = 2,598,960

  3. K selections are made from n items, without regard to order and repeats are allowed. The number of ways these selections can be made is n+K-1CK

  4. Example Number of CD’s to choose from = 10 K = 3 (the number of CD’s that can be ordered) 10+3-1C3 = 12C3 = 12!/3!(12-3)! = 12!/3!9! = 479,001,600/(6)(362,880) = 479,001,600/2,177,280 = 220

  5. When order doesn’t matter, we count the number of subsets or combinations. When order matters, we count the number of sequences or permutations. How many different 7 person committees can be formed, each containing three women from an available set of 20 women, and four men from an available set of 30 men.

  6. Task 1: Choose 3 women from the set of 20 women 20C3 20!/3!(20-3)! = 20!/3!17! = 1140 Task 2: Choose 4 men from the set of 30 men 30C4 30!/4!(30-4)! = 30!/4!26! = 27,405 (1,140)(27,405) = 31,241,700 different committees

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