Question

A question paper is divided into 3 section A, B, C containing 3, 4, 5 question respectively. Find the number of ways of attempting 6 question choosing at least one from each section.

Answer 1

no of combinations= A B C total

1 1 4 6

1 2 3 6

1 3 2 6

1 4 1 6

2 1 3 6

2 2 2 6

2 3 1 6

3 1 2 6

3 2 1 6

$\therefore {}^3{C}_1{\times }^4{C}_1{\times }^5{C}_4+{}^3{C}_1{\times }^4{C}_2{\times }^5{C}_3......+{}^3{C}_3{\times }^4{C}_2{\times }^5{C}_1$

$\Rightarrow 850ways$