(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?

Similar Questions

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

Find the value of $n$ such that $^{n}P_{5} = 42 \, ^{n}P_{3}$,where $n > 4$.

How many numbers greater than $10$ lakh can be formed using the digits $2, 3, 0, 3, 4, 2, 3$?

How many five-digit numbers can be formed using the digits $2, 0, 4, 3, 8$ if repetition of digits is not allowed?

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