The offices or president vice president secretary and treasu

The offices or president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 12 candidates. Five of the candidates are members of the debate team What is the probability that all of the offices are filled by members of the debate team? What is the probability that none of the offices are filled by members of the debate team?

Solution

Given

there are 12 people out of which 5 members are debate team

and there are 4 officers (president, vice presid]ent, secretery and, treasurer)

1)

probebility of all the officers are choosen from debate team = number of ways of choosing 4 officers from debate team / number of wyas of choosing officers from 12 candidates = ⁵C₄ / ¹²C₄ = 5 /495 = 1/99

2)

probebility that no officers are filled by debate team = number of ways of selecting 4 officers from non debate team

candidates / number of ways of selecting 4 officers from 12 candidates = ⁷C₄ /¹²C₄ = 35/495 = 7/99

3)

p(all the offices filled by debate team ) = 1 / 99 = 0.0101 (PROBEBILITY IS CALUCULATED IN CASE 1)