A time traveler can take 5 books with him, and he has 64 books to choose from. H

Question

A time traveler can take 5 books with him, and he has 64 books to choose from. How many different ways can the books be selected? DO NOT put a comma in your response. A casting director wishes to find one male and one female to cast is his play. If he plans to audition 6 males and 15 females, in how many different ways can this be done? DO NOT put a comma in your response. 29 cars are in a race. In how many different ways can cars finish in the top 3 positions? DO NOT put a comma in your response. Evaluate 9C5. DO NOT put a comma in your response. A 5 year old boy has 5 different toys and wants put them all in a straight line. In how many ways can this be done. DO NOT include a comma in your response.

Explanation / Answer

1) Number of different ways 5 books be selected out of 64 = 64C5 = 64! / (5! * (64 - 5)!) = 7624512

2) Number of ways to select 1 male and 1 female = 6C1 * 15C1 = 6 * 15 = 90

3) Number of ways can cars finish intop 3 positions = 29P3 = 29! / (29 - 3)! = 21924

4) 9C5 = 9! / (5! * (9 - 5)!) = 126

5) Number of ways to put the toys in straight line = 5! = 120

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