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.