There are 15 boys and 10 girls in a group discussion. If three students are selected at random, what is the probability that 2 girls and 1 boy are selected?

Step 1: Calculate the total number of students in the group. This is done by adding the number of boys and girls together.

Total students = 15 boys + 10 girls = 25 students

Step 2: Calculate the total number of ways to select 3 students out of 25. This is done using the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items, and r is the number of items to choose.

Total ways to select 3 students = C(25, 3) = 25! / [3!(25-3)!] = 2300 ways

Step 3: Calculate the number of ways to select 2 girls out of 10. This is done using the same combination formula.

Ways to select 2 girls = C(10, 2) = 10! / [2!(10-2)!] = 45 ways

Step 4: Calculate the number of ways to select 1 boy out of 15. This is done using the same combination formula.

Ways to select 1 boy = C(15, 1) = 15! / [1!(15-1)!] = 15 ways

Step 5: Calculate the number of ways to select 2 girls and 1 boy. This is done by multiplying the number of ways to select 2 girls and the number of ways to select 1 boy.

Ways to select 2 girls and 1 boy = Ways to select 2 girls * Ways to select 1 boy = 45 ways * 15 ways = 675 ways

Step 6: Calculate the probability of selecting 2 girls and 1 boy. This is done by dividing the number of ways to select 2 girls and 1 boy by the total number of ways to select 3 students.

Probability = Ways to select 2 girls and 1 boy / Total ways to select 3 students = 675 ways / 2300 ways = 0.293

So, the probability that 2 girls and 1 boy are selected is 0.293 or 29.3%.