Question

RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include Mrs. Vera(only)?

Answer 1

There are 680 combinations of four teachers include Mrs. Vera(only)

How to determine the number of combination?

The given parameters are

Teachers, n = 18

Selected teachers. r = 4

The selection must include Mrs. Vera.

So, the remaining parameters are:

Teachers, n = 17

Selected teachers. r = 3

The combination is then calculated as:

Ways = nCr

This gives

Ways = 17C3

Apply the combination formula

Ways = 17!/(14!3!)

Evaluate the expression

Ways = 680

Hence, there are 680 combinations of four teachers include Mrs. Vera(only)

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