Question

In how many ways $3$ teachers can be invited for a guest lecture on $6$ days in a school so that every teacher is invited atleast once? (On any given day exactly one teacher is invited)

• A. $620$
• B. $540$
• C. $520$
• D. $5040$

Answer 1

Answer: (B)

$540$

Undesired events :

$\bullet$ A single teacher teaches repeately. 3 ways to do so.

$\bullet$ Only two teachers. First choose one of the teacher to exclude him/her, and then we avoid two

extreme cases where one teacher teaches everyday.

$3.(2^6-2)$

Hence the undesired outcomes are

$3(2^6-1)$

Without restriction, we could have $3^6$. Hence

$3^6-3(2^6-1)=3(3^5-2^6+1)=3(243-64+1)=3\left(180\right)=540$