Question

Of the ten students who received an "A+" in a class during the fall 2019 semester, three were sophomores, two were juniors, and one was a senior (the remaining student(s) were in their first year). the teacher believes four of the ten students are strong candidates for TA positions. Determine the probability the four candidates include exactly one student from each year in college.

Answer 1

Total number of students who recieved A+ grade = n = 10

Number of Sophomores = 3
Number of Juniors = 2
Number of Seniors = 1
Number of 1st years = 10 - (3+2+1) = 4

Number of ways to choose 4 candidates such that we get exactly one student from each year

= (No. of ways to choose 1 from 3 Sophomore) x (No. of ways to choose 1 from 2 Juniors) x
(No. of ways to choose 1 from 1 Senior) x (No. of ways to choose 1 from 4 1st year's)

Total number of ways to choose 4 students from 10 students =

Hence, the probability the four candidates include exactly one student from each year in college

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