Question

There are 7 students in a class. If there are 3 seats in the front row, how many ways can the students sit in the front row, assuming there are no empty seats?

Answer 1

35 different ways

Explanation:

Since there are 7 students in a classroom to fill a front row containing 3 seats, we will apply the combination rule since we are to select 3 students from the total number of 7 students in the class.

In combination, if r objects are to be selected from a pool of n objects, this can be done in nCr number of ways.

nCr = n!/(n-r!)r!

Selecting 3 students from 7 students to fill the seats can therefore be done in 7C3 number of ways.

7C3 = 7!/(7-3)!3!

7C3 = 7!/(4)!3!

7C3 = 7*6*5*4!/4!*3*2

7C3 = 7*6*5/6

7C3 = 7*5

7C3 = 35

Hence there are 35 different ways that the student can sit in the front assuming there are no empty seats.