Question

Find the value of n such that :
nP5 = 42 n P3 , n > 4

Answer 1

Answer:

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Step-by-step explanation:

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.