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A boy has 5 cars, 3 trains, and 2 trucks. A) How many ways are there to choose 5 toys from the boy’s collection of toys?
B) How many ways are there to choose 2 cars, 2 trains, and 1 truck?
Thank you in advance!!
4 Answers
- PuzzlingLv 73 years agoFavorite Answer
5 cars, choose 2 --> 5C2 = (5 * 4) / 2 = 10 ways
3 trains, choose 2 --> 3C2 = (3 * 2) / 2 = 3 ways
2 trucks, choose 1 --> 2C1 = 2 ways
10 * 3 * 2
= 60 ways
- 3 years ago
A) 10C5
10! / (5! * (10 - 5)!) =>
10! / (5! * 5!) =>
10 * 9 * 8 * 7 * 6 * 5! / (5! * 5!) =>
10 * 9 * 8 * 7 * 6 / 5! =>
10 * 9 * 8 * 7 * 6 / (6 * 20) =>
9 * 8 * 7 / 2 =>
9 * 4 * 7 =>
63 * 4 =>
252
B)
5C2 * 3C2 * 2C1 =>
5! / (2! * (5 - 2)!) * 3! / (2! * (3 - 2)!) * 2! / (1! * (2 - 1)!) =>
5! * 3! * 2! / (2! * 3! * 2! * 1! * 1! * 1!) =>
5! * 3! * 2! / (3! * 2! * 2!) =>
5! / 2! =>
120 / 2 =>
60
