A student has to choose an elective class for the last semester of high school. His counselor
suggested 8 electives, 6 of which were construction classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all
of them are construction classes?
Write your answer as a decimal rounded to four decimal places.
Submit
Work it out
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First, let's understand what the question is asking. Out of the 8 electives, 6 are construction classes. The student randomly chooses 4 electives to read about. We need to find the probability that all 4 chosen electives are construction classes.

This is a problem of combinations. We need to find:

(Number of ways to choose 4 construction classes) / (Total number of ways to choose 4 electives)

Number of ways to choose 4 construction classes out of 6:

$\dbinom{6}{4} = \frac{6!}{4!(6-4)!} = \frac{6!}{4!2!} = 15$

Total number of ways to choose 4 electives out of 8:

$\dbinom{8}{4} = \frac{8!}{4!(8-4)!} = \frac{8!}{4!4!} = 70$

So, the probability is:

$\frac{15}{70} = \frac{3}{14} \approx 0.2143$

Rounding to four decimal places: 0.2143

Therefore, the probability that all 4 chosen electives are construction classes is 0.2143 or about 21.43%.