Question

An examination paper consists of 12 questions divided into two parts A and B.

Part A contains 7 questions and Part B contains the remaining questions. A candidate required to attempt 8 questions selecting at least 3 from each part. In how many ways can the candidate select the question​

Answer 1

Student has to do 8 questions such that he does at least 3 questions from both the sets

How can he go about (Set I, Set II) =(3,5) or (4,4) or (5,3)

So, total number of ways of doing this is given by

`5c_(3) * 7c_(5) + 5c_(4) * 7c _(4) + 5c_(5) * 7c _(3)`

`= (10)(21) + (5)(35) + (1)(35) = 210 + 210 = 420`

(ノ^_^)ノ

Answer 2

• 420 ways

Explanation:

There are 3 possible scenarios

1) 5 questions from A and 3 questions from B:

• 
  `_7C_5*_5C_3=7!/5!2!*5!/3!2! = (6*7)/2*(4*5)/2=210`

2) 4 questions from each part:

• 
  `_7C_4*_5C_4=7!/4!3!*5!/4!1! = (5*6*7)/(2*3)*5=175`

3) 3 questions from A and 5 questions from B:

• 
  `_7C_3*_5C_5=7!/4!3!*1 = (5*6*7)/(2*3)=35`

Total number of ways:

• 210 + 175 + 35 = 420