Combination SS2 Further Mathematics Lesson Note

Combination can be defined as the number of ways r – objects can be selected from n – objects irrespective of the arrangement

Hence, the notation is thus, nCr or (nr)

, nCr=   n!

         (n-r)!r!

The relationship between permutation and combination is thus, nCr =  nPr    r! 

Example:

1. Evaluate 10C4

Solution:

10C4  = 10!   =  10 x 3 x 7 = 210

         (10-4)!4!

2. In how many ways can three books be selected from 12 books?

Solution:

N = 12, r = 3,   12C3 

=  12!

 (12-3)!3!

     = 12x11x10 = 220 ways

3. A committee consisting of 3 men and 5 women is selected from 5 men and 10 women. Find how many ways this committee can be formed.

Solution:

MEN

R = 3, n = 5

5C3 = 5!

        (5-3)!3!   = 10

WOMEN

r = 5, n = 10

10C5 = 10!

           (10-5)!5!   = 252

Therefore the number of ways of selecting the committee = 10×252 = 2520 ways.

ASSIGNMENT 

1. Find the number of ways the letters of the word FURTHER can be arranged.
2. Find the number of ways of arranging 7 people in a straight line, if two particular people must always be separated.
3. In how many ways can 6 pupils be lined up if 3 of them insist on following one another

Verify that = (n – 1) (n – 2) (n – 3)!