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 =


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