To check if answer is correct, one method is to make an actual list of all the possible combinations.

For class size of 17 and 20, the total ways is too large to list out all the possible combinations.

Have tried with a smaller class size of 7, splitted into 1 group of 3 and 2 groups of 2.

Using the same method of calculation,
total ways =(7C3 x 4C2 x 2C2)/2!
=105
By actual listing out all the possible combinations, have found that it exactly corresponds to the total ways found by calculation.

Therefore, now more confident that the method of calculation used here, is correct.

Thank you!