The number of permutations of letters that can be formed by taking 4 letters at a time from the letters of the word ‘REPETITION’ is

In the word REPETITION

There are R, P, E, E, I, I, T, T, O, N 

Case I : No of 4 letter words using 4 different letters from, {R, P, E, I, T, O, N} $=7_{{\mathrm{P}}_4}=840$

Case II : No of 4 letter wordsusing 2 identical, 2 different letters $=3\times 6_{{\mathrm{C}}_2}\times \frac{4!}{2! }=540$

Case III : No of 4 letter words formed using 2 identical pairs. $=3\times \frac{4!}{2! 2!}=18$

$\boxed{\mathrm{E} \mathrm{E} \mathrm{T} \mathrm{T}} \boxed{\mathrm{E} \mathrm{E} \mathrm{I} \mathrm{I}} \boxed{\mathrm{T} \mathrm{T} \mathrm{I} \mathrm{I}}$

Total no of permutation=840+540+18

                                              =1398