The number of different permutations that can | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The number of integers greater than $3000$ that can be formed by using any number of digits from the set $\{0, 1, 2, 3, 4, 5\}$ without repetition is:

How many $4$-digit numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ such that each digit is used only once?

$60$ words can be made using all the letters of the word $BHBJO$,with or without meaning. If these words are written as in a dictionary,then the $50^{\text{th}}$ word is:

Ten men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

If all the possible $3$-digit numbers are formed using the digits $1, 3, 5, 7, 9$ without repeating any digit,then the number of such $3$-digit numbers which are divisible by $3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module