Mathematics, 21.06.2020 05:57 RedDemon59

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 four different members. There are 14 qualified candidates, and officers can also serve on the committee. A. How many different ways can the officers beappointed?
B. How many different ways can the committee be appointed?
C. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?

Answers: 1

Show answers

Answers

Answer from: nadiareese

a) The officers can be appointed in 24024 different ways.

b) The committee can be appointed in 1001 different ways.

c) 1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

Step-by-step explanation:

The order in which the officers are appointed is important(the first is the president, second the CEO and so on...). So the permutations formula will be used.

Otherwise, in the committee there are no roles, so the order is not important. So the combinations formula will be used.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

A. How many different ways can the officers be appointed?

4 from a set of 14, with roles. So a permutation.

$P_{(14,4)} = \frac{14!}{(14-4)!} = 24024$

The officers can be appointed in 24024 different ways.

B. How many different ways can the committee be appointed?

4 from a set of 14, without roles. So combination

$C_{14,4} = \frac{14!}{4!(14-4)!} = 1001$

The committee can be appointed in 1001 different ways.

C. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes.

The three youngest(1 combination), and one of the other 14-3 = 11. So D = 1*11 = 11

Total outcomes:

From B., 1001, so T = 1001

Probability:

$p = \frac{D}{T} = \frac{11}{1001} = 0.011$

1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

Answer from: Quest

Siciuenckwk the answer

Answer from: Quest

Answer:

$4034.40

step-by-step explanation:

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 13:30, khan2491

2(n-1)+4n=2(3n-1)n=0no solutioninfinitely many solutions n= - 4 !

Answers: 1

continue

Mathematics, 21.06.2019 14:00, williams5847

Chanelle deposits $7,500 into the bank. she does not withdraw or deposit money for 6 years. she earns 6% interest during that time. what will the balance be when she is finally able to withdraw her money?

Answers: 1

continue

Mathematics, 21.06.2019 19:20, cody665

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Answers: 2

continue

Mathematics, 21.06.2019 21:00, blaqsafire404

Timmy uses 1 1 2 cups of sugar for every 2 gallons of lemonade he makes. how many cups of sugar would timmy use if he makes 13 gallons of lemonade?

Answers: 1

continue

You know the right answer?

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO)...