Question

Question #7b172

Answer 1

There are `360` different word codes.

Explanation:

Three I's together positioned within a word of `8` letters can take one of `6` positions:
`123, 234, 345, 456, 567, 678`

Let's count the combinations of other letters for a fixed position of three I's and multiply it by `6`, according to positioning of three I's.

Remaining `5` places are taken by letters D, E, N and two letters T. These letters can be permuted in `5!` different ways, however, we have to divide this number by `2` since exchanging the places between two identical letters T would not change the resulting word.

So, the number of different combinations of D, E, N and two letters T is `(5!)/2 = 60`.
Multiplied by the number of positions of three I's together, the total number of different combinations is `60*6=360`.