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Gaurav Seth 6 years, 10 months ago
Given, total number of questions = 12
Part 1 contains 5 questions and part 2 contain 7 questions.
A student has to select 8 questions all in which there is at least 3 questions from each part.
Now different possibilities can occur.
Part1 (5 questions) Part2 (7 questions)
3 5
4 4
5 3
Now total number of ways is
( 5C3 * 7C5 ) + ( 5C4 * 7C4 ) + ( 5C5* 7C3 )
= ( 5C2 * 7C2 ) + ( 5C1 * 7C3 ) + ( 5C0* 7C3 )
= {(5*4*7*6)/(2*2)} + {(5*7*6*5)/(3*2)} + {(7*6*5)/(3*2)}
= 210 + 175 + 35
= 420
So, the total number of ways a student can select the questions is 420
1Thank You