Question

In CAT entrance examination paper there are 3 sections, each containing 5 questions. A candidate has to solve 5,
choosing at least one from each section. The number of ways he can choose is

Answer 1

i think the number of ways should not be more than \(\large \binom{15}{5} = 3003\)

Answer 2

\[a+b+c = 5\]

\(a,b,c \ge 1\)

Answer 3

http://www.wolframalpha.com/input/?i=3%28%285+choose+1%29%285+choose+1%29%285+choose+3%29+%2B+%285+choose+1%29%285+choose+2%29%285+choose+2%29%29

Answer 4

When the candidate chooses 1 question from each section:
There are 5 choices from the first section. Each of these 5 choices can be combined with each of the 5 choices in the second section. Therefore there are 5 * 5 = 25 ways of choosing a question from each of the first and second sections. Each of these 25 ways can be combined with each of the 5 choices in the third section, giving a total of 25 * 5 = 125 ways of choosing one question from each of the three sections.
When the compulsory single question has been chosen from each of the three sections, there are 12 questions remaining among the three sections from which to choose two more questions, giving 12C2 combinations.
Therefore the number of ways the candidate can choose is given by:
\[\large (5)^{3}\times12C2=8,250\ ways\]

Answer 5

there will be repetitions in your count @kropot72

Answer 6

say the questions are labelled 1-15
1-5 are in first section
6-10 are in second section
11-15 are in third section

below combinations should be counter only one time :
{1,6,11, 2, 7} and {1, 2, 7, 6, 11}

Answer 7

@ganeshie8 Thank you for your explanation, which I understand and agree with.

Answer 8

np :)