The number of words that can be formed by usi | vedclass

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Question

(C) The word $CALCULATE$ has $9$ letters.Out of which $C$ repeats $2$ times,$A$ repeats $2$ times,$L$ repeats $2$ times,and $E, U, T$ appear once.Ther

Vedclass · Accepted Answer

$\frac{5 	imes 7 !}{2}$

Vedclass · Answer

(C) The word $CALCULATE$ has $9$ letters.Out of which $C$ repeats $2$ times,$A$ repeats $2$ times,$L$ repeats $2$ times,and $E, U, T$ appear once.There are $5$ consonants $(C, C, L, L, T)$ and $4$ vowels $(A, A, U, E)$.Two consonants out of $5$ can occupy the start and end positions in $P(5, 2)$ ways.Since there are $2$ $C$'s and $2$ $L$'s,we must account for the repetitions.Total arrangements $= \frac{P(5, 2) 	imes 7!}{2! 	imes 2! 	imes 2!} = \frac{(5 	imes 4) 	imes 7!}{8} = \frac{20 	imes 7!}{8} = \frac{5 	imes 7!}{2}$.

The number of words that can be formed by using the letters of the word $CALCULATE$ such that each word starts and ends with a consonant,are

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