math 30-1 # 3-4-5Permutations and combinations

Verify + P3 = 4PA. a . Left Side Right Side b. Explain how making arrangements using three of four objects can also be thought of as arranging all four objects. 4. A company selling graduation rings currently allows students to customize rings by selecting a ring shape, a gem type, and a metal type. The number of options for each category are listed in the table. Category Number of Options Ring Shape 6 Gem Type 13 Metal Type 4 The company's product team is considering adding an additional option to one category. Which category should be granted the additional option if they want to generate the greatest increase in the number of possible rings? Justify. 5 . A fish tank at the pet store contains 34 fish. If Jake plans to buy 7 fish, in how many different ways can he do this