How many words,with or without meaning,can be | vedclass

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Question

(A) The word $MONDAY$ contains $6$ distinct letters: $M, O, N, D, A, Y$.The number of $4$-letter words that can be formed from these $6$ letters witho

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(A) The word $MONDAY$ contains $6$ distinct letters: $M, O, N, D, A, Y$.The number of $4$-letter words that can be formed from these $6$ letters without repetition is given by the number of permutations of $6$ distinct objects taken $4$ at a time,denoted as $^{6}P_{4}$.The formula for permutations is $^{n}P_{r} = \frac{n!}{(n-r)!}$.Substituting $n=6$ and $r=4$:$^{6}P_{4} = \frac{6!}{(6-4)!} = \frac{6!}{2!} = \frac{6 	imes 5 	imes 4 	imes 3 	imes 2!}{2!} = 6 	imes 5 	imes 4 	imes 3 = 360$.Thus,the total number of words that can be formed is $360$.

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if $4$ letters are used at a time?

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