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.

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Solution

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
$∴^{3} C_{1} \times^{4} C_{1} \times^{5} C_{4} +^{3} C_{1} \times^{4} C_{2} \times^{5} C_{3} . . . . . . +^{3} C_{3} \times^{4} C_{2} \times^{5} C_{1}$
$\Rightarrow 850 w a y s$

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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.

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∴3C1×4C1×5C4+3C1×4C2×5C3......+3C3×4C2×5C1⇒850ways

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
$∴^{3} C_{1} \times^{4} C_{1} \times^{5} C_{4} +^{3} C_{1} \times^{4} C_{2} \times^{5} C_{3} . . . . . . +^{3} C_{3} \times^{4} C_{2} \times^{5} C_{1}$
$\Rightarrow 850 w a y s$