Question

In the following situation, determine whether you are asked to determine the number of permutations or combinations. Then do the calculation. How many ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members?

Answer 1

491400

Explanation:

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

Solution :

Definition of combination: A combination is a collection of the objects where the order doesn't matter

Definition of permutation: A permutation is an arrangement of a group of objects where the order does matter.

since there we need to maintain the order so we will use permutation over here

Since when is selected from 28 members . then next will be selected from remaining 27 and so on.

Since we are required to find ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members

⇒
`_n{P}_r = (n!)/((n-r)!)`

since n = 28

r = 4

So,
`_28{P}_4 = (28!)/((28-4)!)`

`_28{P}_4 = (28!)/((24)!)`

`_28{P}_4 = 28*27*26*25`

`_28{P}_4 = 491400`

Hence in 491400 no. of ways ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members