(C) We have,${}^7P_3 - 3({}^6P_2)$ $= \frac{7!}{(7-3)!} - 3 \times \frac{6!}{(6-2)!}$ $= \frac{7!}{4!} - 3 \times \frac{6!}{4!}$ $= \frac{7 \times 6!}

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(C) We have,${}^7P_3 - 3({}^6P_2)$ $= \frac{7!}{(7-3)!} - 3 \times \frac{6!}{(6-2)!}$ $= \frac{7!}{4!} - 3 \times \frac{6!}{4!}$ $= \frac{7 \times 6!}{4!} - \frac{3 \times 6!}{4!}$ $= \frac{6!}{4!} (7 - 3)$ $= \frac{6!}{4!} \times 4$ $= \frac{6 \times 5 \times 4!}{4!} \times 4$ $= 30 \times 4 = 120$ Alternatively,using the definition of permutation: ${}^6P_3 = \frac{6!}{(6-3)!} = \frac{6!}{3!} = 6 \times 5 \times 4 = 120$ Thus,the value is equal to ${}^6P_3$.

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

Medium

The value of ${}^7P_3 - 3({}^6P_2)$ is equal to

AP EAMCET 2021 All AP EAMCET

A
${}^7P_2$
B
$60$
C
${}^6P_3$
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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