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Find the number of permutation of all th...

Find the number of permutation of all the letters of the word MATHEMATICS which starts with consonants only.

Text Solution

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We have letters (M M), (A A), (T T),H,E,I,C,S
Number of words starting with M to T `=(10!)/(2!xx2!)`
`(because` Two pairs of identical letters are available)
Number of words starting with T or C or S=`(10!)/(2!xx2!xx2!)`
`(because` Three pairs of identical letters are available)
Therefore, total number of words `=2xx(10!)/(2!xx2!)+3xx(10!)/(2!xx2!xx2!)`
`=(7xx10!)/(2!xx2!xx2!)`
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