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

Explanation:

Step1: Calculate total number of ways to choose 4 people

Use combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n=4 + 6=10\), \(r = 4\).

$$C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10\times9\times8\times7}{4\times3\times2\times1}=210$$

Step2: Calculate number of ways to choose 4 seniors

Here \(n = 4\), \(r=4\).

$$C(4,4)=\frac{4!}{4!(4 - 4)!}=1$$

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

$$P=\frac{C(4,4)}{C(10,4)}=\frac{1}{210}\approx0.00476$$

Answer:

0.00476