To find the probability of selecting 1 girl and 2 boys from a class of 15 boys and 10 girls, we can use the concept of combinations.

Step 1: Calculate the total number of ways to select 3 students from a class of 25.

The total number of ways to select 3 students from a class of 25 can be calculated using the combination formula:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of students in the class and r is the number of students to be selected.

In this case, n = 25 and r = 3.

C(25, 3) = 25! / (3! * (25-3)!)
= 25! / (3! * 22!)
= (25 * 24 * 23) / (3 * 2 * 1)
= 2300

Therefore, there are 2300 possible ways to select 3 students from the class of 25.

Step 2: Calculate the number of ways to select 1 girl and 2 boys.

To calculate the number of ways to select 1 girl and 2 boys, we can use the combination formula again.

The number of ways to select 1 girl from a class of 10 is C(10, 1) = 10.

The number of ways to select 2 boys from a class of 15 is C(15, 2) = 105.

Therefore, the number of ways to select 1 girl and 2 boys is 10 * 105 = 1050.

Step 3: Calculate the probability.

The probability of selecting 1 girl and 2 boys can be calculated using the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes (selecting 1 girl and 2 boys) is 1050, and the total number of possible outcomes (selecting 3 students from the class of 25) is 2300.

Probability = 1050 / 2300
= 21 / 46

Therefore, the probability of selecting 1 girl and 2 boys is 21/46, which is option 'C'.