why npr=0 if r>n? give reason
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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
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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.
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