Need help : Permutation and combinations problem.

[Mahmoud Ibrahim]

The student should answer 10 questions out of 13 questions on a condition that he should
answer 4 questions at least from the first 5 questions. How many ways can he answer?
(A) 140 (B) 196 (C) 280 (D) 346
The correct answer is (B) 196 . Please will you explain how to get to this answer. Thanks.

[phw]

I think you need to consider 2 cases.

If you answer 5/5 in the first section and 5/8 in the second, then there are 5C5 * 8C5 ways to choose which questions to answer.

If you answer 4/5 in the first section and 6/8 in the second, then there are (5C4) * (8C6) ways to choose which questions to answer.

[tex]{5 \choose 5}{8 \choose 5} + {5 \choose 4} {8 \choose 6} = 1\cdot56 + 5\cdot28 = 196.[/tex]

[Guest]

Thank you very much. Many many thanks.