Question

The number of permutations of the letters of the word 'INDEPENDENCE' taken 4 at a time so that all the 4 are different is

• A. $24$
• B. $120$
• C. $240$
• D. $360$

Answer 1

The correct option is D $360$

Word INDEPENDENCE has $I-1,N-3,D-2,E-4,P-1,C-1$
There are six different letters in INDEPENDENCE
Now according to question we need to form 4 different letter words,So selection of 4 words out 6 is ${{}^{6}C}_4$ and making its arrangements
So total number of ways is ${{}^{6}C}_4\times 4!=360$