Question

Find the number of ways in which 4 different letters of the word mathematics can be arranged

Answer 1

Given word:   Mathematics

Different letters:   m a t h e i c s

There are 8 different letters out of 10 total.

We need to select 4 different letters and then arrange them in different wars.  This is equivalent to the number of permutations of 4 letters from 8 total.

So the number of ways of selecting 4 out of 8 letters and arranging them in different ways:
       =   8P4  = 8C4 * 4!
       = 8! / 4!
       = 8 * 7 * 6 * 5 /24
       = 70.

Answer 2

Given word:   Mathematics

Different letters:   m a t h e i c s

There are 8 different letters out of 10 total.

We need to select 4 different letters and then arrange them in different wars.  This is equivalent to the number of permutations of 4 letters from 8 total.

So the number of ways of selecting 4 out of 8 letters and arranging them in different ways:

       =   8P4  = 8C4 * 4!

       = 8! / 4!

       = 8 * 7 * 6 * 5 /24

       = 70.

Final Answer :

There can be 70 number of ways.