Sec_2___Counting_Solutions

Sec_2___Counting_Solutions - Section#2 solutions Counting...

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Section #2 solutions Counting Problems: 1. A party has 50 persons. 45 of them are boys. 5 are girls. If we select randomly 6 people, a.) What is the probability to have exactly 1 girl? Pr[Select exactly 1 girl] = ( 29 ( 29 ( 29 45 5 5 1 50 6 0.384 = b.) To have at least 2 girls? Pr[Select at least 2 girls] = 1 – Pr[Select no girls] – Pr[Select exactly 1 girl] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 45 5 45 5 6 0 5 1 50 50 6 6 1 0.103 = - - = 2. There are 20 people at a party. a.) If there are 10 men and 10 women, how many pairs (men with women) are there? # of pairs = 10! 2245 3.63 x 10 6 (Line up women and assign men) b.) If all 20 are men (or women) how many pairs are there? # of pairs = ( 29 ( 29 ( 29 ( 29 20 18 4 2 10 2 2 2 2 20! 2 10! 10! = L 2245 6.55 x 10 8 c.) If there are 10 men and 10 women, but we pair women with women and men with men, how many pairs are there? # of pairs = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 10 8 4 2 10 8 4 2 5 2 2 2 2 2 2 2 2 10! 2 5! 5! 5! � � � � ° = L L 2245 8.9 x 10 5
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3. In a room of n persons, what is the probability two or more people have the same birthday (not necessarily the same year)?
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