Question

Evaluate.

P(7,2)

A.5
B.120
C.21
D.42

Answer 1

\[P(n,r) = \frac{n!}{(n-r)!}\]Do you know how to evaluate factorials?

Answer 2

I forgot. :\

Answer 3

Well, \[n! = n*(n-1)*(n-2)*...(2)(1)\]
so \[5! = 5*4*3*2*1\]etc.

Answer 4

okay

Answer 5

I would advise you take a moment to think before multiplying and dividing all those numbers :-)

For example:
\[\frac{5!}{3!} = \frac{5*4*3*2*1}{3*2*1} = \frac{5*4\cancel{*3*2*1}}{\cancel{3*2*1}} = 5*4\]
I think you'll agree that that is easier to compute than multiplying and dividing the whole bunch, right?

Answer 6

Okay let me see if i can figure out the answer

Answer 7

Is it 42?

Answer 8

@whpalmer4

Answer 9

Yes it is right :)

Answer 10

Thanks

Answer 11

Yep, \[\frac{7!}{(7-2)!} = \frac{7!}{5!} = \frac{7*6*5!}{5!} = \frac{7*6\cancel{*5!}}{\cancel{5!}} = 7*6 = 42\]