{ }^{20}P_5 - { }^{19}P_5 = | vedclass

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Question

(A) We know that ${ }^{n}P_r = \frac{n!}{(n-r)!}$.Given expression is ${ }^{20}P_5 - { }^{19}P_5$.${ }^{20}P_5 = \frac{20!}{15!} = 20 	imes 19 	imes

Vedclass · Accepted Answer

$5 	imes { }^{19}P_4$

Vedclass · Answer

(A) We know that ${ }^{n}P_r = \frac{n!}{(n-r)!}$.Given expression is ${ }^{20}P_5 - { }^{19}P_5$.${ }^{20}P_5 = \frac{20!}{15!} = 20 	imes 19 	imes 18 	imes 17 	imes 16 = 1860480$.${ }^{19}P_5 = \frac{19!}{14!} = 19 	imes 18 	imes 17 	imes 16 	imes 15 = 1395360$.Subtracting the two values: $1860480 - 1395360 = 465120$.Now,check the options:Option $A$: $5 	imes { }^{19}P_4 = 5 	imes (19 	imes 18 	imes 17 	imes 16) = 5 	imes 93024 = 465120$.Thus,the correct option is $A$.

${ }^{20}P_5 - { }^{19}P_5 = $

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