Question

How many ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members?

Answer 1

Answer:

A)$^{28}P_4}=491400$

Step-by-step explanation:

Total number of members = 28

We are supposed to find the no. of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members

When 1 member is selected for Chairman position

So, 27 members will be left for the selection for the position of Vice chairman

When 1 member out of 27  is selected for Vice chairman position

So,26 members will be left for the selection for the position of secretary

When 1 member out of 26  is selected for secretary position

So,25 members will be left for the selection for the position of treasurer

Permutation relates to the act of arranging all the members of a set into some sequence or order,

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.

So, we will use permutation over here

Formula $^nP_r=\frac{n}{(n-r)!}$

Substitute n = 28 and r = 4

So,$^{28}P_4=\frac{28!}{(28-4)!}=491400$

So, Option A is true

A)$^{28}P_4}=491400$

Hence There are 491400 ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members.