Question

The number of permutations by using all the letters of the word $MONDAY$ which neither begins with $M$ nor ends with $Y,$ is

• A. $504$
• B. $696$
• C. $120$
• D. $480$

Answer 1

The correct option is A $504$

Let set $A=$ words beginning with $M$
and set $B=$ words ending with $Y$
Now, we have to find $A^{\prime }\cap B^{\prime }$
$\because A^{\prime }\cap B^{\prime }=(A\cup B{)}^{\prime }$
$n(A\cup B{)}^{\prime }=n(U)-n(A\cup B)$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
Now, $n(A\cup B{)}^{\prime }=n(U)-[n\left(A\right)+n\left(B\right)-n(A\cap B)]$
$=6!-[5!+5!-4!]$
$=504$