How many 8letters code words are possible from the first 16

How many 8-letters code words are possible from the first 16 letters of the alphabet if no letter is repeated? If adjacent letters must be different? There are _ possible 8-letter code words if no letter is repeated.

Solution

we have to select 8 letters from first 16 letters

total number of combinations = 16C₃

each combination can be arranged in 8! ways

so total number 8 letter code words =16C₈ X 8! = 16P₈