Question

Find the number of distinct permutations of the letters in the word MATHEMATICS

Answer 1

Answer:

4989600

step by step explanation:

Step by step workout

step 1 Address the formula, input parameters and values

Formula:

nPr =n!

(n1! n2! . . . nk!)

Input Parameters & Values:

Total number of alphabets (n) & subsets (n1, n2, . . nk) in the word "MATHEMATICS"

n = 11

Subsets : M = 2; A = 2; T = 2; H = 1; E = 1; I = 1; C = 1; S = 1;

n1(M) = 2, n2(A) = 2, n3(T) = 2, n4(H) = 1, n5(E) = 1, n6(I) = 1, n7(C) = 1, n8(S) = 1

step 2 Apply the input parameter values in the nPr formula

=11!

(2! 2! 2! 1! 1! 1! 1! 1! )

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11

{(1 x 2) (1 x 2) (1 x 2) (1) (1) (1) (1) (1)}

=39916800

8

= 4989600

In 4989600 distinct ways, the letters of word "MATHEMATICS" can be arranged.