Choose the calculations that best solve the following counti

Choose the calculations that best solve the following counting problems: a) The Houston Astros must turn in a batting lineup of 9 batters in a specific order. If they have 25 players on the roster, how many different batting orders can be submitted. b) A box contains 25 defective parts of which a sample of 9 will be selected. How many different sample sets are possible? c) A manager of a major grocery store has 25 types of cheese. He wants to place a sample of cheese on each of 9 plates. Assuming repetition is allowed, how many ways can he do this?

Solution

a) ₂₅P₉. Since the different order of batting lineup with same player will be considered as different, for instance (AB) is different from (BA), total number of batting lineup order of 9 batters from a roster of 25 is ₂₅P_9.

b) ₂₅C₉. Total number of sample of size 9 from a population of size 25 is possible in ₂₅C₉ ways.

c) 25⁹. On each of the 9 plates, there is possible to keep any of the 25 cheese. Therefore, total number of ways is 25 x 25 x ...(9 times) = 25⁹.