(C) The word $TRICK$ contains $5$ distinct letters: $T, R, I, C, K$. We need to form a $5$-letter word such that $C$ is fixed in the middle position.

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(C) The word $TRICK$ contains $5$ distinct letters: $T, R, I, C, K$. We need to form a $5$-letter word such that $C$ is fixed in the middle position. This leaves $4$ positions to be filled by the remaining $4$ letters $(T, R, I, K)$. The number of ways to arrange $4$ distinct letters in $4$ positions is given by $4!$. $4! = 4 \times 3 \times 2 \times 1 = 24$. Therefore,there are $24$ possible ways.

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

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Using the letters of the word $TRICK$,a five-letter word with distinct letters is formed such that $C$ is in the middle. In how many ways is this possible?

TS EAMCET 2017 All TS EAMCET

A
$6$
B
$120$
C
$24$
D
$72$

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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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Using the letters of the word $TRICK$,a five-letter word with distinct letters is formed such that $C$ is in the middle. In how many ways is this possible?

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