A company is creating three new divisions and seven managers

A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed? Define the complement of an event (be sure to include notation). Suppose the Florida DMV creates a new license plate for the preservation of the Everglades. The license plate will contain 6 spaces in total, 4 of which will be letters (2 will be single digit numbers). How many license plates can they create if repetition in not allowed?

Solution

Note: we are suppose to answer one question at a time. So i will give you the solution of question 8.

3 new divisions are opeining up and we need to choose 3 heads among 7 people.

we will atke the help of combination

as chosing 3 people among 7 can be represented as 7C3 = 7!/(3!*(7-3)!) = 7!/[3!*4!] = (7*6*5)/(3*2) = 35 WAYS ARE THERE