How many 3-letter words can be formed from th | vedclass

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(C) The word '$EXPERTISE$' consists of $9$ letters: $E, X, P, E, R, T, I, S, E$.Distinct letters available are: $E, X, P, R, T, I, S$. There are $7$ d

Vedclass · Accepted Answer

$210$

Vedclass · Answer

(C) The word '$EXPERTISE$' consists of $9$ letters: $E, X, P, E, R, T, I, S, E$.Distinct letters available are: $E, X, P, R, T, I, S$. There are $7$ distinct letters.Since repetition is not allowed,we need to choose and arrange $3$ letters from these $7$ distinct letters.The number of ways to form a $3$-letter word is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 7$ and $r = 3$.Number of words $= ^7P_3 = 7 	imes 6 	imes 5 = 210$.

How many $3$-letter words can be formed from the letters of the word '$EXPERTISE$',if repetition of letters is not allowed?

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