If 2nP3 = 84. nP2, then the value of n is
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Answer:
Toppr
2n
P
3
=100×
n
P
2
(2n−3)!
2n!
=100×
(n−2)!
n!
(2n−3)!
(2n−3)!(2n−2)(2n−1)2n
=100×
(n−2)!
(n−2)!(n−1)n
2(2n−2)(2n−1)=100(n−1)
(4n−4)(2n−1)=100n−100
8n
2
−4n−8n+4=100n−100
8n
2
−12n+4=100n−100
8n
2
−12n+100−100n+4=0
8n
2
−112n+104=0
4n
2
−56n+52=0
2n
2
−28n+26=0
n
2
−14n+13=0
n
2
−13n−n+13=0
n(n−13)−1(n−13)=0
∴n=1,13
n=1 and 13
n=1 is not possible so
n=13
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