Combination

It is a mathematical technique that determines the possible arrangements in a collection of items where the order of the selection does not matter. In combination, you can select the items in any order.

The number of combinations of a set of n distinct objects taken at a time, is given by

nCr = n!/[(n-r)!r!] ; r =/< n

Where::

C is the total number of COMBINATIONS

n is the total number of distinct objects in the set

r is the total number of choosing objects in the set

Sample Problems: Solve the following combinations.

1. 9C5

2. 14C2

Solutions

1. 9C5 

Given: C =?; n =9; r=5

Formula: nCr = n!/[(n-r)!r!]

Solution:

nCr = n!/[(n-r)!r!]

9C5 = 9!/[(9-5)!5!] 

9C5 = 9!/(4!5!)

9C5 = 9*8*7*6*5!/(4*3*2*1*/5!)

9C5 = 9*2*7/1

9C5 = 126

2. 14C2

Given: C=?; n = 14; r=2

Formula: nCr = n!/(n-r)!r!

Solution:

14C2 = 14!/[(14-2)!2!]

14C2 = 14!/12!2!

14C2 = 14"13"12!/(12!2*1)

14C2 = 7*13

14C2 = 91