A store sells rings with birthstones selected from the 12 different months of the year. The stones are arranged in a row.

Question

Part A: Mary wants a ring with a topaz, a sapphire, and a ruby set in a line. Write and evaluate an expression to show how many ways the 3 stones can be arranged?

Part B: How many permutations are possible with 4 different stones of any month?

Part C: Can more rings be made with 5 different stones than with 4 different stones? Explain.

Answer 1

Part A:
Assuming the ring is not symmetrical, i.e. it cannot be worn both ways, then there are 3! ways the stones can be arranged.
If the ring is symmetrical, divide by 2.

Part B: similar to A, replace 3 by 4.

Part C: Leave it to you as an exercise.