a high school math class has 28 students: 18 seniors and 10 juniors. what is the probability that four…

Answer:

0.17

Explanation:

Step1: Calculate total combinations

The total number of ways to choose 4 students out of 28 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 28$ and $r=4$. So $C(28,4)=\frac{28!}{4!(28 - 4)!}=\frac{28\times27\times26\times25}{4\times3\times2\times1}=20475$.

Step2: Calculate favorable combinations

The number of ways to choose 4 seniors out of 18 is $C(18,4)=\frac{18!}{4!(18 - 4)!}=\frac{18\times17\times16\times15}{4\times3\times2\times1}=3060$.

Step3: Calculate probability

The probability $P$ that 4 randomly - selected students are seniors is $P=\frac{C(18,4)}{C(28,4)}=\frac{3060}{20475}\approx0.17$.