Question

The offices of? president, vice? president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates. Six 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?

Answer 1

The offices of? president, vice? president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates.

That is total number of candidates = n = 15

It is given that 6 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?

First we need to find total and possible ways.

Total ways = select 4 out of 15 =  ¹⁵C₄ = 1365

Possible ways = select 4 out of six = ⁶C₄ = 15

Therefore reuired probability = 15 / 1365 = 3 / 273 = 0.010989

(b) What is the probability that none of the offices are filled by members of the debate? team?

Total ways = 1365

We want to select all four candidates from a non debated cadidates

that is we want to select 4 candidates out of 9 candidates

so possible ways = ⁹C₄ = 126

Therefore required probability = 126 / 1365 = 0.092308