Unformatted text preview: ⋅ 5!)7!/(5! ⋅ 2!) =25221=231 Alternative way is to count directly committees with 1, 2 or three women. The total number will be: C (7,4) ⋅ C (3,1)+ C (7,3) ⋅ C (3,2)+ C (7,2) ⋅ C (3,3)= 3 ⋅ 7!/(4! ⋅ 3!)+3 ⋅ 7!/(3! ⋅ 4!)+7!/(2! ⋅ 5!)= 3 ⋅ 35+3 ⋅ 35+21=231. 3) (10pts). In how many ways a card hand consisting of 3 spades and 2 hearts can be selected from a standard 52card deck? 3 spades can be selected in C (13,3) different ways. 2 hearts can be selected in C (13,2) different ways. By the product rule the total number of hands is C (13,3) ⋅ C (13,2)=(13 ⋅ 12 ⋅ 11) ⋅ (13 ⋅ 12)/(3 ⋅ 2 ⋅ 2)=286 ⋅ 78...
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 Spring '09
 Playing card, total number, dozen brown socks, dozen black socks

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