You are a restaurant manager You must pick 12 entrees for yo

You are a restaurant manager. You must pick 12 entrees for your menu. There are 12 meat offerings and 7 poultry offerings to choose from. Order doesn\'t matter. In how many ways can 12 entrees be randomly selected out of the 19 meat and poultry offerings? Show work. In how many ways can 12 entrees be chosen, if 7 must be meat and 5 must be poultry? Show work. Using your answers to parts (a) and (b), if 12 entrees are randomly selected from the 19 offerings, what is the probability that 7 are meat and 5 are poultry? Round answer to nearest ten-thousandth (4 places after decimal). Show work.

Solution

a)   12 entrees randomly selected out of 19 meat and poultry offerings

19C12 = 19!/( 12!)(7!) = 50388

b) 7 must be meat , we have 12 meat offerings ---12C7

5 must be poultry , we have 7 poultry offerings --- 7C5

So, no. of ways 12 entrees can be selected are--- 12C7*7C5 = 792*21 = 16632

c) Probability of 12 entrees randomly selected from 19 offerings are = 12C7*7C5 /19C12

                                                                           = 16632/ 50388

                                                                            = 0.3301