Find the number of combinations of the for objects A,B,C,D taken three at a time . How many committees of three can be formed from eight people.

We'll write the formula of the combination of n elements
taken k at a time:

C(n,r) =
n!/k!(n-k)!

We'll establish that each
combination consists of 3 objects.

We'll have 3!
permutations of objects in the combination.

We'll note the
permutation as P.

P = 3!

P =
1*2*3

P = 6

The number of
combinations will be multiplied by 3!:

C(4,3) =
P(4,3)/3!

P(4,3) =
4*3*2

P(4,3) = 24

C(4,3) =
24/6

C(4,3) = 4

The possible
combinations are:

C(4,3) = {abc , abd , acd ,
bcd}

To determine the number of committees
of three that can be formed from eight people, we'll apply the combination
formula:

C(8,3) =
8!/3!(8-3)!

C(8,3) =
8!/3!*5!

But 8! = 5!*6*7*8

3!
= 1*2*3

C(8,3) =
5!*6*7*8/1*2*3*5!

We'll simplify and we'll
get:

C(8,3) =
7*8/1

C(8,3) = 56 committees of three that
can be formed from eight people.