Math Help Forum: Counting problem

Let S = {1,2,3,4,5}
(a) List all the 3-permutations of S
(a) List all the 3-combinations of S

Can any one help me with this ??

Originally Posted by bhuvan

Let S = {1,2,3,4,5}
(a) List all the 3-permutations of S
(a) List all the 3-combinations of S

Can any one help me with this ??

a) 5C3 = 5!/(3!*(5-3)!) = 10 (order doesn't matter)
b) 5P3 = 5!/(5-3)! = 60 (order matters)

a)
{1,2,3}
{1,2,4}
{1,2,5}
{1,3,4}
{1,3,5}
{1,4,5}
{2,3,4}
{2,3,5}
{2,4,5}
{3,4,5}
Total = 10



b)
{1,2,3}
124
125
132
134
135
142
143
145
152
153
154
.
.
.
should add up to 60

Hello, bhuvan!

Let

(a) List all the 3-permutations of

There are of them.

I'll start the list . . .

. .

(b) List all the 3-combinations of

There are of them . . .

. . .


Edit: . Ha! TitaniumX beat me to it . . .
.

thank you very much ...

How many solutions are there to the equation

x1+x2+x3+x4=17

where x1,x2,x3 and x4 are nonnegative integers ??

appreciate your reply.

Originally Posted by bhuvan

How many solutions are there to the equation
x1+x2+x3+x4=17. where x1,x2,x3 and x4 are nonnegative integers ??

The number of ways to put N identical ones into k different variables (non-negative integers) is .
Here N=17 and k=?

can you please give me one example of that ??