in how many ways can the letters of MATHEMATICIAN be arranged if the arrangment must begin with c and end with a?

Question

in how many ways can the letters of MATHEMATICIAN be arranged if the arrangment must begin with c and end with a?

Answer 1

MATHEMATICIAN is 13 letter word

 

As first and last letter is decided we can arrange 11 letter

 

If C is first and A is last letter

 

There are 11 letter

 

There are 2 M

 

There are 2 A ( 3rd A is last letter)

 

There are 2 T

 

There are 2 I

 

 

 

11! / 2!*2!*2!*2!

 

=39916800/16

 

= 2494800