Question

There are 15 technicians and 11 chemists working in a research lab. They need to form a 5 person safety committee. In how many ways can this committee be formed if it can be chosen in any way?

Answer 1

There are a total 65,780 ways in which the committee can be made of 5 members.

Step-by-step explanation:

Here, the total number of technicians in the lab = 15

The total number of chemists in the lab  = 11

So, the total members in the lab  = 15 + 11 = 26

So, there are total 26 eligible candidates in the lab from which committee of 5 people has to be made.

Now, since there is no restrictions on the choice, so the committee can be formed in nay way, such that:

It may or may not have any technician.

It may or may not have may chemists.

So, the number of ways 5 member can randomly be chosen from a committee of 26 people  = $^{26} C_5$

$^{26} C_5$ = $^{26} C_5 = \frac{26!}{5! \times 21!} = 65,780$

Hence, there are a total 65,780 ways in which the committee can be made of 5 members.