I notice that the sequence must have a fixed format: L _ _ Q. This means that I only have to choose the middle two letters from the remaining four letters: E, U, A, and S. I also notice that the order of the middle two letters matters, since swapping them would create a different sequence. So, I need to count the number of ways to arrange two letters out of four, without repetition. This is a permutation problem, and I recall that the formula for permutations of n objects taken r at a time is nPr = n! / (n - r)!. In this case, n = 4 and r = 2, so I plug those values into the formula and get 4P2 = 4! / (4 - 2)! = 4! / 2! = 24 / 2 = 12. Therefore, there are 12 possible sequences of four letters that satisfy the given conditions. 
How many distinct sequences of four letters can be made from the letters in EQUALS if each sequence must begin with L, end with Q, and no letter can appear in a sequence more than once?