Combinatorics: In how many ways can members be chosen?

[jshaziza]

A club consists of 30 men and 70 women. In how many ways can a president, vice-president, secretary, and sergeant-at-arms be chosen if the president must be a woman, the sergeant-at-arms must be a man, and one person cannot hold more than one office.

Would I seperate the different scenarios and than multiply like,
70C1 for the president, 30C1 for the sergeant-at-arms, and than 100C1 for the vice-president and secretary. 70C1x30C1x100C1x100C1. Is this correct?

By the way what I mean by 70C1 is 70 denoted C 1 denoted.

 

[arthur ohlsten]

you must remember after choosing a president and a sgt at arms you only have 98 people left, not 100.

30 men
70 woman

from the 70 woman choose a president, AND, from the 30 men choose a sgt at arms,AND, from the remaining 98 choose a Vice President,AND from the remaining 97 choose a secretary

when you say AND multiply, when you say OR, add

70C1 * 30C1 * 98C1 * 97C1

If you were to choose 2 people and then decide which is to be the secretary and vice president
70C1 * 30C1 * 98C2

Arthur