A hint to get started
Arrange adjacent letters and form CELEBRATE codewords
(a) Find the number of different arrangements of the nine letters in CELEBRATE in which A and T are next to each other.
(b) Find the number of 3-letter codewords that can be formed from the letters of CELEBRATE.
[2008/IJC/II/6]
CJC · Lecture · Example 14
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.