The number of different permutations that can be formed by taking 4 letters at a time from the letters of…
The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word 'REPETITION' is
1380
1218
1398
1286
Solution
Given letters are $\mathrm{E}, \mathrm{E}, \mathrm{I}, \mathrm{I}, \mathrm{T}, \mathrm{T}, \mathrm{R}, \mathrm{P}, \mathrm{O}, \mathrm{N}$.
Case-I : If all four letters are different then number of four word letters $={ }^7 P_4=840$
Case II : If two letters are same and two letters are different then number of words $={ }^6 C_2 \times \frac{4!}{2!} \times 3=540$
Case-III : If two letters are one type and another two letters are other same type $=3 \times \frac{4!}{2!2!}=18$
So, total ways $=840+540+18=1398$.