1. n!
4 x 3 x 2 x 1 = 24

2. 10! =
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =
3,628,800
5! =
5 x 4 x 3 x 2 x 1 =
120

3. nPr 5P2 6P4 ORDER n! (n – r)! n r 5! 5! 5 x 4 x 3 x 2 x 1    = 20
order is imPortant n!
nPr
(n – r)! n r 5! 5!
5 x 4 x 3 x 2 x 1
5P2    = 20
(5 – 2)! 3!
3 x 2 x 1 n r 6! 6!
6 x 5 x 4 x 3 x 2 x 1
6P4    =
360
(6 – 4)! 2!
2 x 1

4. n r
ORDER
matters 10
nPr
4 =
5040 r n
ORDER
matters 8
nPr
3 =
336

5. nCr 10C4 nCr order n! r!(n – r)! n r 10! 10!   4!(10 – 4)! 4!( ) 6!
No one Cares about the order n!
nCr
r!(n – r)! n r
10!
10!
10C4  
4!(10 – 4)!
4!( ) 6!
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
5040 = =
210
4 x 3 x 2 x 1 x
6 x 5 x 4 x 3 x 2 x 1 24 n r 5
nCr
2 = 10

6. P =
336 8 3 C = 10 5 3 C =
5,461,512 60 5 C =
4,845 20 4 P = 24 4 4

7. 1 1 C 38,760 1 1 P 380 r n   r n   20 6 20 2 order does NOT matter
fraction
order
does
NOT matter 1 1 ?
part
whole   C
38,760 20 6 r n
fraction
order ? 1 1
does
matter
part
whole   P
380 20 2