# 6.3 Combinations

6.3 Combinations

(1) The number of combinations of r objects chosen from n different
objects is given by :
$\overline{){}^{n}{C}_{r}=\frac{n!}{r!\left(n-r\right)!}}$

(2) A combination of r objects chosen from n different objects is a
selection of a set of r objects chosen from n objects. The order of
the objects in the chosen set is not taken into consideration.

Example 1:

Calculator Computation:

Example 2:
There are 6 marbles, each with different colour, which are to be divided equally between 2 children. Find the number of different ways the division of the marbles can be done.

Solution:
Number of ways giving 3 marbles to the first child =  ${}^{6}{C}_{3}$

Number of ways giving the remaining 3 marbles =  ${}^{3}{C}_{3}$

So, the number of different ways the division of the marbles