Question

an archaeology club has 55 members. How many different ways can the club select a​ president, vice​ president, treasurer, and​ secretary?

There are ____ different slates of candidates possible.

Answer 1

This question can be solved by the method of permutation and combination.

It has two parts :

1). We need to choose president , vice president ,treasurer and secretary . There are chances of replacement in every count , a person being president can be treasurer or anything else. So we need to use ' permutation method to slove this we get

(55 P 4 ) = (55!÷4!) =55×54×53×52 = = 8,185,320ways. (ANSWER)

2 ). In second part of the question we need to find the no. Of different slates or simply say, we require to find different no. of groups of these 4 people.

So we need to use combination method

(55 C 4 ) = ( 55! ÷ ( 4! × 51!). = 341,055 ways (ANSWER)

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