Q18 of 30 Page 7

Find r if :  (i) 5Pr = 2 6Pr-1   (ii) 5Pr = 6Pr-1


(i) P(5,r) =

2P(6,r-1) = 2

Given P(5,r) = 2P(6,r-1)

= 2

= 2 dividing by 5!

=

= 1

12 = r2-13r+42

r2-13r-30 = 0

(r - 10)(r - 3) = 0 , r = 10 or 3

Given P(5, r), and since 10 >5, r = 10 is not possible.

Thus, r = 3

(ii) P(5,r) =

P(6,r-1) =

Given =  

=

=

1 =

r2 - 13r + 42 = 6

r2 - 13r + 36 = 0

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

r = 9 or 4

Given P(5, r) and P(6, r-1) r=9 not possible as r >5, thus  r=4.

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