Answer:
The probability that all of the offices are filled by members of the debate team is 0.0512 and the probability that none of the offices are filled by members of the debate team is 0.0256
Step-by-step explanation:
The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates.
So, Number of candidates required = 4
Total number of candidates = 15
Number of candidates which are members of the debate team. = 8
So, Number of candidates which are not the members of the debate team = 15-8 =7
The probability that all of the offices are filled by members of the debate team = [tex]\frac{^8C_4}{^{15}C_4}=\frac{\frac{8!}{4!\left(8-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0512[/tex]
The probability that none of the offices are filled by members of the debate team=[tex]\frac{^7C_4}{^{15}C_4}=\frac{\frac{7!}{4!\left(7-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0256[/tex]
Hence The probability that all of the offices are filled by members of the debate team is 0.0512 and the probability that none of the offices are filled by members of the debate team is 0.0256
