An examination paper with 10 questions consists of 6 questions in Algebra and 4 questions in geometry. At least two questions from each section is to be attempted. In how many ways can this be done?

 We need to attempt atleast two questions from algebra, means we can attempt 2,3,…6 questions from algebra.

⁶C₂+⁶C₃+⁶C₄+⁶C₅+⁶C₆=2⁶-1–6 (using binomial theorem)

Similarly for algebra we have 2⁴-1–4 choices.

So total number of ways are -

(2⁶-1–6)(2⁴-1–4)=57*9=513