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 0.08824.
(b) all women. round your answer to five decimal places.
the probability that the group consists of all women is

Explanation:

Step1: Calculate the number of ways to choose 4 students from 17

The formula for combinations 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 number of ways to choose 4 women from 7

Using the combination formula with \(n = 7\) and \(r = 4\)

$$C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7\times6\times5}{3\times2\times1}=35$$

Step3: Calculate the probability

The probability \(P\) that the group consists of all women is the number of ways to choose 4 women divided by the number of ways to choose 4 students.

$$P=\frac{C(7,4)}{C(17,4)}=\frac{35}{2380}\approx0.01471$$

Answer:

\(0.01471\)