How many permutations can be made out of the letters of the word triangle. How many of these will begin with t and end with e?

Explanation

There are 8 letters in the word triangle.

(1) Total number of ways of permutations are to put these 8 letters in 8 places=`8_(P_8)​ `

=`(8!)/(0!)​=8! =40320
`
2)Word beginning with t and ending with e implies that 2 positions out of 8 are fixed.
So we need to arrange 6 letters in 6 positions.


Number of permutations =`6_(P_6)​ =(6!)/(0!)​=6! =720`