(A) The word $UNIVERSAL$ consists of $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.To form a word of $3$ letters from these $9$ distinct letters,w

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(A) The word $UNIVERSAL$ consists of $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.To form a word of $3$ letters from these $9$ distinct letters,we use the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 9$ and $r = 3$.Required number of words $= ^9P_3 = \frac{9!}{(9-3)!} = \frac{9 \times 8 \times 7 \times 6!}{6!} = 9 \times 8 \times 7 = 504$.

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

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How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?

A
$504$
B
$405$
C
$540$
D
$450$

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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 comprising of any three letters of the word $UNIVERSAL$ can be formed?

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