In how many ways can we select a committee of 3 boys and 2 girls form a class of 12 boys and 16 girls?
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Question 4 6 pts
A bucket contains 6 black, 4 white and 5 green balls. In how many ways can 3 ball be selected if
(a) 2 balls are black and 1 is white
(b) 3 balls are green
(c) at least 2 balls are black
In how many ways can we select a committee of 3 boys and 2 girls form a class of 12 boys and 16 girls?
2016-08-09 4:31 am
回答 (2)
2016-08-09 4:37 am
12C3 * 16C2
12! * 16! / (3! * 2! * (12 - 3)! * (16 - 2)!) =>
12! * 16! / (6 * 2 * 9! * 14!) =>
12 * 11 * 10 * 9! * 16 * 15 * 14! / (12 * 9! * 14!) =>
11 * 10 * 16 * 15 =>
11 * 240 * 10 =>
2640 * 10 =>
26400
You start with 15 balls
6 * 5 * 4
5 * 4 * 3
3 * 6 * 5 * 13 + 6 * 5 * 4
12! * 16! / (3! * 2! * (12 - 3)! * (16 - 2)!) =>
12! * 16! / (6 * 2 * 9! * 14!) =>
12 * 11 * 10 * 9! * 16 * 15 * 14! / (12 * 9! * 14!) =>
11 * 10 * 16 * 15 =>
11 * 240 * 10 =>
2640 * 10 =>
26400
You start with 15 balls
6 * 5 * 4
5 * 4 * 3
3 * 6 * 5 * 13 + 6 * 5 * 4
2016-08-09 4:33 am
26400 ways
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