In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

To solve this problem, we need to use the concept of combinations from probability theory.

Step 1: Calculate the total number of students in the class. There are 15 boys and 10 girls, so the total number of students is 15 + 10 = 25.

Step 2: Calculate the total number of ways to select 3 students out of 25. This is a combination problem, which can be solved using the formula for combinations: C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, the total number of ways to select 3 students out of 25 is C(25, 3) = 25! / [3!(25-3)!] = 2300.

Step 3: Calculate the number of ways to select 1 girl out of 10 and 2 boys out of 15. This is also a combination problem. The number of ways to select 1 girl out of 10 is C(10, 1) = 10, and the number of ways to select 2 boys out of 15 is C(15, 2) = 105. So, the total number of ways to select 1 girl and 2 boys is 10 * 105 = 1050.

Step 4: Calculate the probability. The probability is the number of favorable outcomes (selecting 1 girl and 2 boys) divided by the total number of outcomes (selecting any 3 students). So, the probability is 1050 / 2300 = 0.4565, or 45.65% when expressed as a percentage.

To solve this problem, we need to use the concept of combinations from probability theory.

Step 1: Calculate the total number of students in the class. There are 15 boys and 10 girls, so the total number of students is 15 + 10 = 25.

Step 2: Calculate the total number of ways to select 3 students out of 25. This is a combination problem, which can be solved using the formula for combinations: C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, the total number of ways to select 3 students out of 25 is C(25, 3) = 25! / [(25-3)! * 3!] = 2300.

Step 3: Calculate the number of ways to select 1 girl out of 10 and 2 boys out of 15. This is also a combination problem. The number of ways to select 1 girl out of 10 is C(10, 1) = 10, and the number of ways to select 2 boys out of 15 is C(15, 2) = 105. So, the total number of ways to select 1 girl and 2 boys is 10 * 105 = 1050.

Step 4: Calculate the probability. The probability is the number of favorable outcomes (selecting 1 girl and 2 boys) divided by the total number of outcomes (selecting any 3 students). So, the probability is 1050 / 2300 = 0.4565, or approximately 45.65%.