00:01
In this problem, first of all, we have been asked how many different committees of size three can be formed from 15 people.
00:07
So out of 15 people, any three need to be selected at random.
00:11
This can be done in 15 c3 ways.
00:13
Here we use c, which represents combination, and we use combination and not permutation in this case because the order of selection of the people does not matter.
00:21
So what is the formula for ncr? this is n factorial over r factorial times n minus r factorial.
00:29
So in this case n is 15, r is 3, so we have 15 factorial over 3 factorial times the factorial of 15 minus 3, which is 12, and this is equal to 455.
00:40
So the required answer is 455.
00:44
Now next we have been asked to determine the number of ways three offices can be filled if we have a certain committee which consists of 16 people...