A four-symbol locker code with repeats allowed

Question

A gym locker opens with a code of 4 symbols in order. Each symbol is one of 6 shapes, and the same shape may be reused in different slots. How many different codes are possible?

Accepted Answer

Fill the code one slot at a time. Because repeats are allowed, every slot has the full set of 6 shapes available, independently of the others: 6 	imes 6 	imes 6 	imes 6 = 6^4 = 1296. The key twist versus a "no-repeats" problem is that earlier choices do not remove options from later slots. Each of the 4 positions keeps all 6 shapes, so the count is a power rather than a shrinking product. Takeaway. When repetition is allowed and the choice set stays the same size, the count is (options) raised to the (number of slots): here 6^4 = 1296.

A four-symbol locker code with repeats allowed

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