Q25 of 31 Page 7

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

A student has to attempt 8 questions in total and at least 3 from each part.


There can be three cases:


Case 1: 3 from part 1 and 5 from part 2


5C3 × 7C5





= 10× 21


= 210 ways


Case 2: 4 from part 1 and 4 from part 2


5C4 × 7C4





= 5× 35


= 175 ways


Case 3: 5 from part 1 and 3 from part 2.


5C5 × 7C3





= 35 ways


So total ways = 210 + 175 + 35


= 420 ways


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iii) do all the vowels never occur together


iv) do the words begin with I and end in P?