Class 11

Math

Algebra

Permutations and Combinations

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

- 2250
- 30240
- 22660
- None of these

Hence $E_{′}s=3$ $S_{′}s=2$

Hence the required combination is

the coefficient of $x_{5}$ in

$5![(1+x+2!x_{2} +3!x_{3} )(1+x+2!x_{2} )(1+x)_{4}]$

Simplifying , we get the coefficient as

$10(36+96+72+21)$

$=10×225$

$=2250$