Question

Some students at Penn State decide to form a new club for Anime enthusiasts.

A new club is formed

They were able to gather 25 people in total(including themselves). They decide to create a board to handle the club functionalities.

a) They decide to create a board committee of 4 people. In how many ways can it be done? __________

b) Let's say the board decides to have the following designations: President, Technical Head, Event Head and Treasurer. In how many ways can these positions be filled so that no person can hold more than 1 position? _________

Answer 1

Ans:

Total no. of people=25

(a).

Here we need a Board Committee with 4 people.

so we can select in 25C₄ ways.

No. of ways it can be done=25C₄ = 12650 ways.

(b)

We have Desinations,

President, Technical Head, Event Head and Treasurer

Here, no person can hold more than one position.

so, these 4 designations can be filled in 25C₁*24C₁*23C₁​​​​​​​*22C₁​

here for 2nd and next desinations we decreased from 25 ro 24, 23 and 22.

Because if one person is alloted to 1st designation then we have 24 only and again another person is alloted to 2nd designation then we have only 23 people like wise..

No. of ways = 25C₁*24C₁​​​​​​​*23C₁​​​​​​​*22C₁​​​​​​​​​​​​​​ = 25*24*23*22 = 303600 ways