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(C) The word '$REPETITION$' contains $10$ letters: $R, E, E, P, E, T, I, T, I, O, N$. The distinct letters are ${R, E, P, T, I, O, N}$,where $E, I, T$

Vedclass · Accepted Answer

$1398$

Vedclass · Answer

(C) The word '$REPETITION$' contains $10$ letters: $R, E, E, P, E, T, I, T, I, O, N$. The distinct letters are ${R, E, P, T, I, O, N}$,where $E, I, T$ repeat twice each.Case-$I$: All $4$ letters are different.We choose $4$ letters from $7$ distinct letters ${R, E, P, T, I, O, N}$ and arrange them: $^7P_4 = 7 	imes 6 	imes 5 	imes 4 = 840$.Case-$II$: $2$ letters are the same and $2$ are different.We choose $1$ pair from $3$ available pairs ${E, E}, {I, I}, {T, T}$ and $2$ letters from the remaining $6$ distinct letters: $^3C_1 	imes ^6C_2 	imes \frac{4!}{2!} = 3 	imes 15 	imes 12 = 540$.Case-$III$: $2$ letters are of one type and $2$ are of another type.We choose $2$ pairs from $3$ available pairs: $^3C_2 	imes \frac{4!}{2!2!} = 3 	imes 6 = 18$.Total permutations $= 840 + 540 + 18 = 1398$.

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

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