(B) The word $DHOLPUR$ contains $7$ distinct letters: $D, H, O, L, P, U, R$. If $L$ and $P$ are excluded,we are left with $7 - 2 = 5$ distinct letters

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(B) The word $DHOLPUR$ contains $7$ distinct letters: $D, H, O, L, P, U, R$. If $L$ and $P$ are excluded,we are left with $7 - 2 = 5$ distinct letters: $D, H, O, U, R$. We need to form words of $4$ distinct letters using these $5$ letters. The number of ways to arrange $r$ objects out of $n$ distinct objects is given by $^nP_r = \frac{n!}{(n-r)!}$. Here,$n = 5$ and $r = 4$. Number of words = $^5P_4 = \frac{5!}{(5-4)!} = \frac{120}{1} = 120$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

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

A
$24$
B
$120$
C
$144$
D
$240$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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

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