How many four-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?

This is the concept of combination. The number of letter-sequence that are possible to be formed from the letters q,u,a,k,e,s will be evaluated as follows:
Total number of letters is 6
Maximum number of letters in a word is 4
thus the number of four letter sequence that can be formed will be:
6C4
=15
The reason why we are using combination is because no letter can be used more than once in each sequence.