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Permutation problems reward students who identify the restriction before they begin counting.
In this example, a sequence consists of three pentoses (5-carbon sugars) and five hexoses (6-carbon sugars), with the condition that a hexose must be placed on each end. Once those positions are filled, the remaining sugars can be arranged using factorials to determine the total number of possible sequences.
Give the problem a try before looking at the solution, and let us know how you approached it.
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