Permutations and combinations

Question 5: A committee that consists of 6 members is to be selected from 5 teachers and 4 students. Find the number of different committees that can be formed if (a) there is no restriction, (b) the number of teachers must exceed the number of students. Solution: (a) Total number of committees = 5 + … Read more

Question 1: The diagram below shows five cards of different letters. R E A C T (a) Calculate the number of arrangements, in a row, of all the cards. (b) Calculate the number of these arrangements in which the letters E and A are side by side. Solution: (a) Number of arrangements = 5! = 120 (b)  Step … Read more

4.3 Combinations(1) The number of combinations of r objects chosen from n different objects is given by : n C r = n ! r ! ( n − r ) ! (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 … Read more

(C) Permutation of n Different Objects, Taken r at a Time 1. The number of permutations of n different objects, taken r at a time is given by:   2.  A permutation of n different objects, taken r at a time, is an arrangement of a set of r objects chosen from n objects. The … Read more

(A) rs Multiplication Principle/ Rule 1. If an operation can be carried out in r ways and another operation can be carried out in s ways, then the number of ways to carry out both the operations consecutively is r × s, i.e. rs. 2. The rs multiplication principle can be expanded to three or more … Read more