A candidate is required to answer 6 out of 10 questions which are divided into two groups each containing 5 questions and he is not permitted to attempt more than 4 from each group. In how many ways can he make up his choice?

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Solution

Group A 5, Group B 5. Questions to be attempted 6 but not more than 4 from any group (4A,2B), (3A,3B), (2A, 4B).
$^{5} C_{4}$ x $^{5} C_{2}$ + $^{5} C_{3}$ x $^{5} C_{3}$ x $^{5} C_{2}$ x $^{5} C_{4}$
= 50 + 100 + 50 = 200.

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