Question

Total no. Of different words (meaningful or meaningless) that can be formed using all the letters of the word MATHEMATICS is k, then k/11×7! is ________

Answer 1

let $W$ be the word "MATHEMATICS", which has a length $L = 11$

Assuming each letter from the word can only be used once,

total number of words is

$L! = L * (L-1) * (L-2) * (...) * (2) * (1) = 11! = 11*10!$

so, if k = L!,

$\frac{k}{11*7!}= \frac{L!}{11*7!} \\\\=\frac{11 * 10!}{11*7!}\\\\= \frac{10!}{7!}\\\\= 720$

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