Question

Four seniors and six juniors are competing for four places on a quiz bowl team. What is the approximate probability that all four seniors will be chosen at random? 0.00020 0.00476 0.06667 0.07142

Answer 1

Answer: Second Option

$P =0.00476$

Step-by-step explanation:

The probability sought is calculated by calculating the quotient between the number of possible ways to select 4 seniors from a group of 4 seniors among the number of ways to select 4 seniors from a group of 10 people.

So:

$P =\frac{4C4}{10C4}$

Where

$nCr = \frac{n!}{r!(n-r)!}$

is the number of ways in which a number r of people can be selected from a group of n people

Then

$P =\frac{\frac{4!}{4!(4-4)!}}{\frac{10!}{4!(10-4)!}}\\\\\\P =\frac{1}{\frac{10!}{4!(10-4)!}}\\\\P =\frac{1}{210}\\\\P=0.00476$