If ^9P_5 + 5 . ^9P_4 = ^10P_r , then r = ?

Permutations Practice Test 1

Question : 12 of 40

Marks: +1, -0

^9P_5 + 5 . ^9P_4 = ^10P_r

, then

r = ?

Solution:

From the given relation,

9!/4!+5 . 9!/5!=10!/{(10-r)!}

⇒2/4×9!=10×9!/(10-r)!

⇒ (10 - r)! = 5 . 4! = 5!

⇒ 10 - r = 5 ⇒ r = 5

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