# Counting

1. A computer science society has 67 members.

How many ways are there to choose 6 members of the society to serve on an executive committee?

2. A computer science society has 31 members.

How many ways are there to choose a chairman, vice chairman, and treasurer of the society?

(Assuming that the 1st selected person will serve as chairman, the 2nd, and 3rd selected persons will serve as vice chairman and treasurer, respectively.)

3. 7 persons are chosen at random from a group of 19 persons consisting of men and women. 4 of the women are sisters. Find the number of ways that the 7 persons chosen include the 4 sisters.

最好俾埋步驟，

感激不盡！

### 1 Answer

- YYLv 61 decade agoFavorite Answer
1)

67!

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6! x (67 - 6)!

= 99795696

2)

31 x 30 x 29 = 26970

3)

(19 - 4)!

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(7-4)! (19-4-7+4)!

= 910