A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 17 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below.

a. How many different ways can the officers beappointed?
There are__different ways to appoint the officers.
b. How many different ways can the committee be appointed?
There are___different ways to appoint the committee.
c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?
P(getting the three youngest of the qualified candidates)=
(Type an integer or a simplified fraction.)

a) 57120 ways

b) 4080

c= nothing

Step-by-step explanation:

Total number of qualified candidates= 17

Total number of officers to be appointed =4

Number of different ways using permutation = 17C4=57120

b) Total number of qualified candidates =17

Total number of planning officers=3

Number of different ways using permutation = 17C3=4080 ways

C) Probability P(getting 3 youngest of the qualified candidates)= nothing

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.