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Question

Solve:
nP4n1P5=3.

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Solution

Given,

nP4n1P5=3

or, n(n1)(n2)(n3)(n1)(n2)(n3)(n4)(n5)=3

or, n=3(n4)(n5)

or, 3n227n+60=n

or, 3n228n+60=0

or, 3n218n10n+60=0

or, 3n(n6)10(n6)=0

or, (3n10)(n6)=0.

Since n is a natural number then n=6.


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