Question

in a class of 17 students, there are 10 men and 7 women. four students are selected to present a demonstration on the use of graphing calculators. find the probability that the group consists of (a) all men. round your answer to five decimal places. the probability that the group consists of all men is

Explanation:

Step1: Calculate the combination of choosing 4 students from 17

The formula for combination is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 17\) and \(r=4\).

$$C(17,4)=\frac{17!}{4!(17 - 4)!}=\frac{17\times16\times15\times14}{4\times3\times2\times1}=2380$$

Step2: Calculate the combination of choosing 4 men from 10

Here \(n = 10\) and \(r = 4\)

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

Step3: Calculate the probability

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

$$P=\frac{C(10,4)}{C(17,4)}=\frac{210}{2380}\approx0.08824$$

Answer:

\(0.08824\)