How many different words can be formed with the letters of the word 'CAPTAIN'? In how many of these C and T are never together ?

Answer

2520, 1800

Explanation

The given word 'CAPTAIN' has 7 letters, out of which there are 2 A's and the rest are all different.
Number of their arrangements `=(7!)/(2!)=2520.`
Let us assume CT as 1 letter.
Then CT + APAIN has 6 letters, out of which there are 2 A's and the rest are all distinct.
Number of their arrangements `=(6!)/(2!)=360.`
Also, CT can be arranged among themselves in 2! = 2 ways.
Number of arrangements in which C and T are together `=(360xx2)=720.`
Number of arrangements in which C and T are never together `=(2520-720)=1800.`