Question

why npr=0 if r>n? give reason

Answer 1

nPr = 0 if r > n

There are two ways to understand this.

First of all, nPr means in how many ways, we can permutate r objects out of n objects.

Now, if r > n, suppose r = 5 and n = 3

Then how can you permutate 5 objects out of 3 objects? I mean, in order to permutate, first of all you'll need to take 5 objects out of 3 objects, which is not humanly possible.

If you don't get it, don't worry there's a mathematical approach too, which is discussed in the attachment

Answer 2

Answer:

☆Given:-

nPr= n!

(n-r)!

☆To prove:-

▪why nPr=0 ,r>n ? give reason .

Proof:-

▪We want here to prove that nPr=0,r>n

▪so we know that

n

p = n !

r (n-r)!

▪r>n, n-r is negative quantity

▪suppose if we take n =5 and r=6

5

p = 5!

6 (5-6)!

= 5!

(-1)i

= 5i × 1!

(-1)!

= 5!×0

=0.

☆Hence proved .

☆Hope it helps u mate.

☆Thank you.