practice problems pending

Q1. Find the number of ways in which 30 marks can be allotted to 8 questions if each question carries at least 2 marks?
S1.
x1 + ... x8 = 30-16 = 14
Stars and bars, n = 14, k = 8
14+8-1C8-1 = 21C7

Q2. In an exam the maximum marks for each of three papers is 'n' and that for fourth paper is 2n. Find the number of ways in which a student can get (3n) marks.

S2.





Using negative binomial expansions:





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