Question

HMUCI Uldil 23. Corporate Officers and a III UL arranged. Find that number. ate Officers and Committees The Digital Pet Rock Company was recently suc- lly funded via Kickstarter and must now appoint a president, chief executive officer co chief operating officer (COO), and chief financial officer (CFO). It must also appoint strategic planning committee with four different members. There are 10 qualified candidates. and officers can also serve on the committee. a. How many different ways can the four officers be appointed? b. How many different ways can a committee of four be appointed? c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

Answer 1

(a)

The four officers can be chosen out of the 10 qualified candidates in 10! 4°C4 = 4!(10 – 4)1 = 4161 = 210 ways. 10!

(b)

The four committee members can be chosen out of the 10 qualified candidates in 10! 10! 4°C4 = 4!(10 – 4)1 = 4161 = 210 ways.

[We consider all 10 candidates for choosing the committee members since officers can also serve on the committee.]

(c)

We can choose the four youngest of the qualified candidates in 1 way. :. Probability of randomly selecting the committee members and getting the four youngest of the qualified candidates = number of ways of selecting the committee members 210