Question

Find the number of words that can be formed by using all the letters of the word ${}^{\prime }DIFFERENTIATIO{N}^{\prime }$

• A. $15!$
• B. $4!.3!.2{!}^4$
• C. $\frac{15!}{3!\times 2{!}^4}$
• D. none of these

Answer 1

The correct option is C $\frac{15!}{3!\times 2{!}^4}$

Given word $DIFFERENTIATION=15$ letters.

We have repeated letters $-I$($3$ times ) $,F\left(2\right),E\left(2\right),N\left(2\right),T\left(2\right)$

Total permutations $=\frac{15!}{3!2!2!2!21}$

$=\frac{15!}{3!(2!{)}^4}$

Hence, the answer is $\frac{15!}{3!(2!{)}^4}.$