How many words of 4 distinct letters can be f | vedclass

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Question

(C) The word $DHOLPUR$ contains $7$ distinct letters: $D, H, O, L, P, U, R$.We need to form a $4$-letter word that must include $L$ and $P$.Since $L$

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(C) The word $DHOLPUR$ contains $7$ distinct letters: $D, H, O, L, P, U, R$.We need to form a $4$-letter word that must include $L$ and $P$.Since $L$ and $P$ are already selected,we need to choose $2$ more letters from the remaining $5$ letters $(D, H, O, U, R)$.The number of ways to choose these $2$ letters is $^5C_2 = \frac{5 	imes 4}{2 	imes 1} = 10$.Now,we have $4$ letters ($L, P$ and the $2$ chosen letters),which can be arranged in $4!$ ways.$4! = 4 	imes 3 	imes 2 	imes 1 = 24$.Therefore,the total number of words is $10 	imes 24 = 240$.

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ such that $L$ and $P$ are always included?

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