Answer:
Probability: [tex]\frac{1}{24310}[/tex]
Step-by-step explanation:
There are two methods:
1. Fraction method (Longer expression)
2. Combination method (Shorter expression)
Fraction method:
We want the numerator to be the number of students remaining and the denominator to be the total number of individuals (students + faculty) remaining after each selection.
[tex]\frac{8}{17}*\frac{7}{16} *\frac{6}{15} *\frac{5}{14} *\frac{4}{13} *\frac{3}{12} *\frac{2}{11} *\frac{1}{10} = \frac{1}{24310}[/tex]
Multiplying the fractions mean they are in the same combination during one single selection process.
Combination method:
Most calculators should have a permutation and combination function. We will use combination as there is no specific order in selecting students.
[tex]\frac{8C8*9C0}{17C8} = \frac{1}{24310}[/tex]
Pretend the C means "Choose", We want to choose all 8 students and 0 faculty, therefore "8 choose 8" for students and "9 choose 0" for faculty. Lastly divided by "17 (total individuals) choose 8 (students only)" to make it into a probability, similar to the fraction method but way shorter.
