Question

egra i b-cr
twelve education students, in groups of four, are taking part in a student-teacher program. mark cannot be in the first group because he will be arriving late.
how many ways can the instructor choose the first group of four education students?
○ 220
○ 330
○ 1,980
○ 7,920

Explanation:

Step1: Identify valid student count

Total students: 12, exclude Mark → 11 students eligible.

Step2: Use combination formula

We choose 4 from 11, formula: $\binom{n}{k}=\frac{n!}{k!(n-k)!}$
Substitute $n=11, k=4$:
$$\binom{11}{4}=\frac{11!}{4!(11-4)!}=\frac{11\times10\times9\times8}{4\times3\times2\times1}$$

Step3: Calculate the value

$\frac{11\times10\times9\times8}{24}=330$

Answer:

330