Question

If np5 =42np3, then n=...
a) -10
b) 9
c) 10
d) 4​

Answer 1

Answer:

4

Step-by-step explanation:

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Answer 2

Option c

Step-by-step explanation:

Given:-

np5 =42np3

To find:-

Find the value of n?

Solution:-

Given that

np5 =42np3

We know that

npr =n!/(n-r)!

np5 = n!/(n-5)!

np3 = n!/(n-3)!

n!/(n-5)! = 42×n!/(n-3)!

On cancelling n! both sides

=>1/(n-5)! = 42×1/(n-3)!

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

=>(n-5)! = (n-3)/42!

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

On Cancelling (n-5)!

=>1= (n-3)(n-4)/42

=>1×42 = (n-3)(n-4)

=>(n-3)(n-4)=42

=>n(n-4)-3(n-4)=42

=>n^2-4n-3n+12 = 42

=>n^2-7n+12 = 42

=>n^2-7n+12-42=0

=>n^2-7n-30=0

=>n^2+3n-10n-30=0

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

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

=>n+3 = 0 or n-10=0

=>n = -3 or n=10

n can not be negative

So, n= 10

The value of n = 10

Answer:-

The value of n for the given problem is 10

Used formula:-

• npr =n!/(n-r)!