Question

can you please explain the proof of why nPr = n!/(n-r)! for me please?

Answer 1

say you have n distinct objects and you need to fill up r places. so the first place can be filled up in n ways, second place can be filled up in (n-1) ways and so on.. the r th place can be filled up in (n-r+1) ways, so number of patterns formed= n*(n-1)*(n-2)*.....(n-r+1), that is nothing but nPr

Answer 2

now, we know n!= n*(n-1)*(n-2).....*1
nPr= n*(n-1)*(n-2)......*(n-r+1)
with nPr, first multiply (n-r)*(n-r-1)...*1 and divide by the same quantity.
so, numerator will be n*(n-1)....*(n-r+1)*(n-r)*(n-r-1)...*1= n!
denominator will be (n-r)*(n-r-1)....*1=(n-r)!
so, nPr= n!/(n-r)!

Answer 3

You may need to define nPr if you want a rigorous proof.

Answer 4

yeh why do u multiply and then divide it?? (line 3 of the second post)