Question

Algebraically show that n P r = (n C r) X (r P r) and describe the significance of this relationship in your own words.

Answer 1

nPr = n! / ( n-r ) !
nCr = n! / [ (n-r)! r! ]
r P r = r! / ( r-r)! ,
and 0! = 1, n! = n* ( n-1)!

Answer 2

so putting it together we have
nPr = n! / ( n-r ) !
nCr x rPr = n! / [ (n-r)! r! ] *r! / ( r-r)!