Question

Two teachers are interviewing top $6$ students in FTRE exam, in two different subjects stating at the same time. Each teacher interview for $15$ minutes; the number of ways in which interview can be scheduled is

• A. $6!$
• B. $5!$
• C. $44\times 6!$
• D. $265\times 6!$

Answer 1

The correct option is D $265\times 6!$

There are $6$ students to be interviewed by $2$ teachers. Lets say each teacher has $6$ slots to interview $6$ students. These interviews can be done in $6!$ ways.

Now, the same student cannot be at $2$ interviews simultaneously, So the other teacher must be interviewing anybody except the one that is already in the other interview. This is a problem of dearrangement.

$\Rightarrow$ No. of dearrangements $=6!(1-\frac{1}{1!}+\frac{2}{2!}-......\frac{1}{6!})$

$\Rightarrow$ Total $=6!\times [6!(\frac{1}{1!}+......\frac{1}{6!}\left)\right]=6!\times 265$

Hence, the answer is $6!\times 265.$