Question

the offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 17 candidates. eight of the candidates are members of the debate team.
(a) what is the probability that all of the offices are filled by members of the debate team?
(b) what is the probability that none of the offices are filled by members of the debate team?

(a) p(all offices filled by debate team members) =
(round to three decimal places as needed.)

(b) p(no offices filled by debate team members) =
(round to three decimal places as needed.)

Explanation:

Determine the total number of outcomes

Using the Permutations vs Combinations knowledge point

$$ N = P(17, 4) = \frac{17!}{(17-4)!} = 17 \times 16 \times 15 \times 14 = 57,120 $$

Calculate probability for part (a)

Using the Hypergeometric Probability and Permutations vs Combinations knowledge points

$$
LATEXBLOCK0
$$

Calculate probability for part (b)

Using the Hypergeometric Probability and Permutations vs Combinations knowledge points

$$
LATEXBLOCK1
$$

Answer:

Question 1

(a) P(all offices filled by debate team members) = <blank>0.029</blank>

Question 2

(b) P(no offices filled by debate team members) = <blank>0.053</blank>