(B) The word "$ASSASSINATION$" contains $13$ letters in total: $3$ $A$'s,$4$ $S$'s,$2$ $I$'s,$2$ $N$'s,$1$ $T$,and $1$ $O$. To keep all $4$ $S$'s toge

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(B) The word "$ASSASSINATION$" contains $13$ letters in total: $3$ $A$'s,$4$ $S$'s,$2$ $I$'s,$2$ $N$'s,$1$ $T$,and $1$ $O$. To keep all $4$ $S$'s together,we treat them as a single block or unit,say $Z$. Now,we have the letters: $A, A, A, I, I, N, N, T, O, Z$. This gives us $10$ items to arrange,where $A$ repeats $3$ times,$I$ repeats $2$ times,and $N$ repeats $2$ times. The number of arrangements is given by $\frac{10!}{3! 2! 2!}$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In how many ways can the letters of the word "$ASSASSINATION$" be arranged so that all $S$'s are together?

AP EAMCET 2022 All AP EAMCET

A
$10!$
B
$\frac{10!}{3! 2! 2!}$
C
$\frac{9!}{3! 2! 2!}$
D
$9!$

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In how many ways can the letters of the word "$ASSASSINATION$" be arranged so that all $S$'s are together?

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