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How many arrangements can be made …

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How many arrangements can be made with the letters of the word MATHEMATICS (I) order of vowels remain unchanged

Posted by Pankaj Swaroop 4 years ago

CBSE > Class 11 > Applied Maths

1 answers

Yogita Ingle 4 years ago

(i) There are 11 letters in the word 'MATHEMATICS' . Out of these letters M occurs twice, A occurs twice, T occurs twice and the rest are all different.
Hence, the total number of arrangements of the given letters
=11!/ (2!)×(2!)×(2!)=4989600.
(ii) The given word contains 4 vowels AEAI as one letter, we have to arrange 8 letters MATHMTCS + AEAI, out of which M occurs twice, T occurs twice and the rest are all different.
So, the number of all such arrangements =8!/ (2!)×(2!)=10080
Now, out of 4 vowels, A occurs twice and the rest are all distinct.
So, the number of arrangements of these vowels =4!/2!=12
Hence, the number of arrangement in which 4 vowels are together =(10080×12)=120960.

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