combinations & permutations?

Question

a) Combinations
There are 12 candidates for 4 positions

C(m,n)= __M !_______
(m - n)! n!

b) Permutations
There is 52 cards. How many hands you can deal taken five in each hand?

P(m,n)= ___m !________
(m - n)!

Answer 1

The ! means factorial. If it is 5! then that means 5*4*3*2*1 = 120.
so for a) that would be 12!/8!4!
for the numerator, that's 12*11*10*9*8*7*6*5*4*3*2*1
and for the denominator, it's 8*7*6*5*4*3*2*1*4*3*2*1
you can cancel out the 8*7*6*5*4*3*2*1 and have
12*11*10*9 over 4*3*2*1
then 12 cancels with 4*3 and 10 cancels with the 2 leaving
11*5*9 over 1 or 495

for b) it is 52!/47!
you know that's going to cancel out the 47*46*45..., so all you are going to have left is 52*51*50*49*48

Answer 2

12C4 = 12!/(8!*4!) = 12*11*10*9/24 = 4950

52P5 = 52!/47!=52*51*50*49*48 = 311,875,200