Question

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

Answer 1

Mark cannot be in the first group, so the instructor must pick 4 students from the other 11. That gives C(11,4) = 330.

(Alternatively: total C(12,4)=495 minus those containing Mark C(11,3)=165, so 495−165=330.)