Suppose you\'re a master jeweler who makes rings. A customer orders a custom-mad

Question

Suppose you're a master jeweler who makes rings. A customer orders a custom-made ring consisting of five gemstones. You have 10 identical diamonds, 6 identical emeralds, 5 identical sapphires, and 3 identical rubies. You also have silver, gold and platinum from which the ring can be constructed. A ring consists of a choice of the metal and however many gemstones requested by the costumer.

a) How many different rings can you make for this customer, assuming no other restrictions?

b) Whst is the probability that the ring will be platinum with atleast 2 rubies?

Explanation / Answer

a)

Total number of possible rings = 24C5 * 3 = (24!/(5!*19!))*3 = 127512 Answer

3 for metal choices.
24C5 for choosing 5 out of 24 gems.

b)

Number of rings of platinum with atleast 2 rubies = 3C2 * 22C3 = 3* (22!/(19!*3!))= 4620

Probability that the ring will be platinum with atleast 2 rubies = 4620/127512 = 0.0362 Answer

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