1.

104. What is the value of r ifP(5, r) P(6 r-1) ?

Answer»

P(5,r) = P(6,r-1)

We know that P(n,r) = n!/(n-r)!

=> 5!/(5-r)! = 6!/(6-r+1)!

=> (7-r)!/(5-r)! = 6!/5! (By rearranging terms)

Also n! = n(n-1)!

=> (7-r)(6-r)(5-r)!/(5-r)! = 6×5!/5!

=> (7-r)(6-r) = 6 (Cancelling terms)

=> r^2 - 13r + 36 = 0

=> (r-9)(r-4) = 0

Hence r = 4,9


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