Question

. If 2nP3 = 100 x n P2, find t n.
​value​

Answer 1

Answer:

A]

2n

P

3

=100×

n

P

2

=

(2n−3)!

(2n)!

=100×

(n−2)!

n!

=

(2n−3)!

(2n−3)!(2n−2)(2n−1)2n

=

(n−2)!

100×(n−2)!(n−1)n

=2(2n-2)(2n-1)=100(n-1)

=2(4n

2

−6n+2)=100n−100

=8n

2

−12n+4=100n−100

=8n

2

−112n+104=0

=4n

2

−56n+52=0

=2n

2

−28n+26=0

==n

2

−14n+13=0

= n (n-13) - 1 (n-13) = 0

n = 1, n = 13

∴ n = 13 [as n=1 not possible]

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