Question

Find the value of n such that nP5=42 * nP3 N is greater than 4

Answer 1

ⁿP₅=42×ⁿP₃
or, n!/(n-5)!=42×n!/(n-3)!
or, 1/(n-5)!=42/(n-3)(n-4)(n-5)!
or, 1=42/(n²-3n-4n+12)
or, n²-7n+12=42
or, n²-7n-30=0
or, n²-10n+3n-30=0
or, n(n-10)+3(n-10)=0
or, (n-10)(n+3)=0
Either, n-10=0
or, n=10
Or, n+3=0
or, n=-3
∵, n can not be negative ;
∴, n=10 Ans.

Answer 2

ⁿP₅=42×ⁿP₃

n!/(n-5)!=42×n!/(n-3)!

1/(n-5)!=42/(n-3)(n-4)(n-5)!

1=42/(n²-3n-4n+12)

n²-7n+12=42

n²-7n-30=0

n²-10n+3n-30=0

n(n-10)+3(n-10)=0

(n-10)(n+3)=0

Either, n-10=0

or, n=10

Or, n+3=0

or, n=-3

∵ n can not be negative

∴ n=10