Permutation

[Guest]

In a Chemistry test, John has two papers, A and B, containing 7 and 11 questions
respectively. He has to attempt 12 questions in total, selecting at least 4 from each paper.
How many ways can John select a question? ( In the book : The answer is 16401 )
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I think the solution is : from paper A : ( 7 * 6 * 5 * 4 ) = 840
And from paper B : ( 11 * 10 * 9 * = 7920
The rest questions from paper A are 3 and from paper B are 7 , they are ( 3 + 7 = 10 questions)
The student can select four questions from those 10 : (10 * 9 * 8 * 7) = 5040
The total are : 840 + 7920 + 5040 = 13800.
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Please , what is the mistake in my solution. Thanks.

[romsek]

In a Chemistry test, John has two papers, A and B, containing 7 and 11 questions
respectively. He has to attempt 12 questions in total, selecting at least 4 from each paper.
How many ways can John select a question? ( In the book : The answer is 16401 )
-------------------------------------------------------
I think the solution is : from paper A : ( 7 * 6 * 5 * 4 ) = 840
And from paper B : ( 11 * 10 * 9 * = 7920
The rest questions from paper A are 3 and from paper B are 7 , they are ( 3 + 7 = 10 questions)
The student can select four questions from those 10 : (10 * 9 * 8 * 7) = 5040
The total are : 840 + 7920 + 5040 = 13800.
--------
Please , what is the mistake in my solution. Thanks.

You're multiplying the wrong things together.

[tex]N = \sum \limits_{k=4}^7~\dbinom{7}{k}\dbinom{11}{12-k} = 16401[/tex]

[Guest]

Thank you very much. I didn't study this formula. I will try to find it in any math site. Thanks again.