Question

how many different words can be formed of the letters of the words MATHEMATICS so that no vowels are together​

Answer 1

Answer:

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Answer 2

Answer:

In the word “ MATHEMATICS” there are 7 consonants (2 M's ,2 T's ,1H, 1C, 1S ) and 4 vowels ( 2 A's , 1E, 1I) .

First we will arrange the consonants as the are 2 M and 2T's so ways of arrangement = 7!/2!2!

And now among those 7 consonants , there are 8 gaps, where we can fill vowels.

_M_T_H_M_T_C_S_

There are 4 vowels and 8 gaps so the ways of selecting 4 gaps out of 8 gaps =8C4

And ways of arranging them i.e. 2A's, 1E and 1I =4!/2!

Hence the total ways of arrangement so that's no two vowels come together =(7!/2!2!)8C4(4!/2!) = 1,058,400 ways