Lennie Carroll

2020-12-06

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

rogreenhoxa8

Skilled2020-12-07Added 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,

$nPr=\frac{n!}{n1!n2!\dots nk!}$

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,

${n}_{1}\left(M\right)=2,{n}_{2}\left(A\right)=2,{n}_{3}\left(T\right)=2,{n}_{4}\left(H\right)=1,{n}_{5}\left(E\right)=1,{n}_{6}\left(I\right)=1,{n}_{7}\left(C\right)=1,{n}_{8}\left(S\right)=1$

Step 4

The input parameters are applied based on the nPr formula as follows,

$=\frac{11!}{2!2!2!1!1!1!1!1!}$

$=\frac{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10\times 11}{(1\times 2)(1\times 2)(1\times 2)\left(1\right)\left(1\right)\left(1\right)\left(1\right)\left(1\right)}$

$=\frac{39916800}{8}$

Step 5

On dividing the value as,

$=\frac{39916800}{8}=4989600$

Hence, the letters of word "MATHEMATICS" 4989600 distinct ways of arrangement.

Given:

The different letter arrangements are calculated from the word MATHEMATICS as follows,

Step 2

The formula is calculated as below,

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,

Step 4

The input parameters are applied based on the nPr formula as follows,

Step 5

On dividing the value as,

Hence, the letters of word "MATHEMATICS" 4989600 distinct ways of arrangement.

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