Question 2102

A group of students is to be chosen to represent three schools, A,B{A,B} and C.{C.} The group is to consist of 12 students, and is chosen from a set of 18 students consisting of 5 from A{A}, 6 from B{B} and 7 from C{C}. Find the number of ways in which the group can be chosen if it includes

(a) (2 marks) 3 students from A{A}, 3 students from B{B} and 6 students from C{C},

(b) (2 marks) students from B{B} and C{C} only,

(c) (2 marks) at least 6 students from C{C},

(d) (4 marks) at least 1 student from each school.

This question is inspired by the 2008 A Levels H2 Mathematics Paper 2 Question 10.
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