COMBINATION: Selection, Conditional Selection And Its Application

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)


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 in the following one another

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



Read permutation and combination, further mathematics project 2 pages 47-54



1.                  Evaluate 6C2 + 6C3 + 6C4 + 6C5 (a) 6C6 (b) 6C5 (c) 8C5

2.                  How much ways can the letters of the word EVALUATE be arranged? (a) 10080 (b) 20160 (c) 40320

3.                  In how many ways can 2 boys and 3 girls be arranged to sit in a row, if the boys must sit together (a) 6 (b) 4 (c) 24

4.                  Find the number of ways 6 people can be seated in a round table, if two particular friends must sit next to each other (a) 48 9b) 24 (c) 120

5.                  In how many ways can 6 pupils be lined up if 3 of them insist on following one another? (a) 720 (b) 144 (c) 24



1.                  Out of 7 lawyers, 5 judges, a committee consisting of 3 lawyers, 2 judges is to be formed, in how many ways can this be done, if

a.                   Any lawyer and any judge can be included

b.                  One particular judge can be included

c.                   Two particular lawyer cannot be in committee

2.                  If nP3 / nC2 = 6, find the value of n

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