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 = \(\frac{n!}{r!s!t!}\)
(i) Here n = 5
P is repeated twice
So the number of permutations = \(\frac{5!}{2!}\) = 5 x 4 x 3 = 60
(ii) Here n = 7
A is repeated twice, and R is repeated twice
So, the number of permutations = \(\frac{7!}{2!2!}\) = \(\frac{7\times6\times5\times4\times3}{2}\) = 1260
(iii) Here n = 8
M and E are repeated twice
So, the number of permutations = \(\frac{8!}{2!2!}\) = \(\frac{8\times7\times6\times5\times4\times3\times2}{4}\) = 10080
(iv) Here n = 9
I is repeated twice, T is repeated thrice
So, the number of permutations = \(\frac{9!}{2!2!}\) = 30240
(v) Here n = 11
E, N is repeated thrice, I,G are repeated twice
So the number of permutations = \(\frac{11!}{3!3!2!2!}\) = 277200
(vi) Here n = 12
I and T are repeated twice, E is repeated thrice
So, the number of permutations = \(\frac{12!}{2!2!3!}\) = 19958400