To solve the problem of finding the number of ways to make a group of 4 students without including the class monitor, follow these steps:

1. Identify the total number of students available for selection excluding the class monitor.
   Since the class monitor cannot be included, we have 9 students left (10 total - 1 class monitor).

2. Calculate the number of ways to choose 4 students from the 9 remaining students.
   This is a combination problem, and the formula for combinations is given by:

   $\text{Number of combinations} = \binom{n}{r} = \frac{n!}{r!(n-r)!}$

   Here, $n = 9$ and $r = 4$.

   $\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = \frac{3024}{24} = 126$

Therefore, the number of ways to form a group of 4 students without including the class monitor is 126.

The correct answer is (b) 126.

Would you like to see the details or have any questions? Here are some related questions you might find useful:

1. How do you calculate combinations when choosing multiple objects?
2. What is the difference between combinations and permutations?
3. How would the answer change if we wanted to include the class monitor in every group?
4. How many ways can you form a group if the group size was 5 instead of 4?
5. How would the problem change if there were two class monitors, and neither could be included?

Tip: Remember, combinations are used when the order of selection does not matter, whereas permutations are used when the order does matter.