Question

Find the number of permutations and combinations of 4 letters taken from the word examination

Answer 1

Sol: There are 11 letters not all different.They are AA,II,NN,E,X,M,T,O. The following combinations are possible: 1) Number of ways selecting 2 alike,2 alike = 3c2 = 3 ways. 2) Number of ways selecting 2 alike,2 different = 3c1 x 7c2 = 3 x 21 = 63 ways. 3) Numkber of ways selecting all 4 different = 8c4 = 70 ways. ∴ Total number of combinations = 3 + 63 + 70 = 136 ways. ∴Total number of permutations (1) to (3) = 3 x(4!/2!2!) +63 x (4!/2!) +70 x4! = 18 + 756 + 1680 = 2454.