Suppose 6 people are invited for job interviews. 2 Monday, 2 Wednesday, 2 Saturday

Question

Suppose that 6 people are invited for job interviews.

How many different ways are there for 2 to be interviews on Monday, 2 on Wednesday, and 2 on Saturday?

Is this as simple as $\frac {6!} {2! 2! 2! } $?

Thank you for the help in confirming.

Answer 1

You are correct.

Another approach: Two of the candidates can be selected to interview on Monday in $\binom{6}{2}$ ways. Two of the remaining four candidates can be selected to interview on Wednesday in $\binom{4}{2}$ ways. The remaining two candidates must be interviewed on Saturday. Hence, the number of possible interview schedules is $$\binom{6}{2}\binom{4}{2} = \frac{6!}{2!4!} \cdot \frac{4!}{2!2!} = \frac{6!}{2!2!2!}$$ as you found.

Answer 2

You are inviting 2 people in a day, for 3 days. This is similar to dividing 6 objects into three equal groups of 2.

So total number of possible ways =

$$\frac {6!}{2! 2! 2!} = 90 $$