Find the total number of permutations of the letters of each of the words given below:
(i) APPLE (ii) ARRANGE
(iii) COMMERCE (iv) INSTITUTE
(v) ENGINEERING
(vi) INTERMEDIATE
To find: number of permutations of the letters of each word
Number of permutations of n distinct letters is n!
Number of permutations of n letters where r letters are of one kind, s letters of another kind, t letters of a third kind and so on =
(i) Here n = 5
P is repeated twice
So the number of permutations =
(ii) Here n = 7
A is repeated twice, and R is repeated twice
So, the number of permutations =
(iii) Here n = 8
M and E are repeated twice
So, the number of permutations =
(iv) Here n = 9
I is repeated twice, T is repeated thrice
So, the number of permutations =
(v) Here n = 11
E, N is repeated thrice, I,G are repeated twice
So the number of permutations =
(vi) Here n = 12
I and T are repeated twice, E is repeated thrice
So, the number of permutations =