Question

The number of permutations of the letters of the word EXERCISES taken 5 at a time is

• A. 2250
• B. 30240
• C. 22660
• D. None of these

Answer 1

The correct option is A 2250

Given word is $EXERCISES$
Hence $E^{\prime }s=3$ $S^{\prime }s=2$
Hence the required combination is
the coefficient of $x^5$ in
$5!\left[\right(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}\left)\right(1+x+\frac{x^2}{2!}\left)\right(1+x{)}^4]$
Simplifying , we get the coefficient as
$10(36+96+72+21)$
$=10\times 225$
$=2250$