The offices of? president, vice? president, secretary, and treasurer for an environmental club will be filled from a pool of 17 candidates. nine 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

we are given

total number of candidates =17

Nine of the candidates are members of the debate team

number of debate candidates=9

(a)

Total number of officers=4

we can use combination formula

So, the number of ways in which 4 people can be selected from 17 people is

now, we can simplify it

and the number of ways in which 4 people can be selected from the debate team of 9 is

now, we can simplify it

so, P(all offices filled by debate team members) is

so, P(all offices filled by debate team members) is  0.0529..........Answer

(b)

non-debate team is 17-9=8

number of ways in which 4 people can be selected from the non-debate team of 8 is

Probability that none of the office is filled by the debate team is

..............Answer

the answer is d

hope this