How many different letter arrangements can be made from the letters in the word MATHEMATICS?

Lennie Carroll 2020-12-06 Answered
How many different letter arrangements can be made from the letters in the word MATHEMATICS?
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Expert Answer

rogreenhoxa8
Answered 2020-12-07 Author has 109 answers
Step 1
Given:
The different letter arrangements are calculated from the word MATHEMATICS as follows,
Step 2
The formula is calculated as below,
nPr=n!n1!n2!nk!
Step 3
The value of the input parameters and values as follows,
The alphabets having the total number is n and the subset follows the values as (n1, n2, . . nk) based on the word "MATHEMATICS" with the value of n=11
The subsets are as follows,
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 4
The input parameters are applied based on the nPr formula as follows,
=11!2!2!2!1!1!1!1!1!
=1×2×3×4×5×6×7×8×9×10×11(1×2)(1×2)(1×2)(1)(1)(1)(1)(1)
=399168008
Step 5
On dividing the value as,
=399168008=4989600
Hence, the letters of word "MATHEMATICS" 4989600 distinct ways of arrangement.

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