Question

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasure will be filled. In how many different ways can the offices be filled?

Answer 1

Here total candidates =12.

We have to filled president , vice president , secretary and treasure from these 12 candidates.

Hence we can to filled 4 seats form 12 candidate.

Here order we need to use permutations

Total different ways can the offices be filled is,

ⁿP_k = ¹²P₄ = ​ = ​​11880.

Therefore ,

Total different ways can the offices be filled is 11880.

Another method.

Total choice available for first post 12

Total choice available for second post 11 (as one is filled on furst post)

Total choice available for third post 10

And similarly total choice acailavai for fourth post is 9

So total different ways =12*11*10*9=11880.