Q. 115.0( 1 Vote )
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
Answer :
Given that 10 questions are to be answered by part A and part B by choosing at least 4 from each part.
It is also mentioned that there are 6 questions in part A and 7 in part B.
There are 3 cases to answer 10 questions:
i. 4 from part A and 6 from part B
ii. 5 from part A and 5 from part B
iii. 6 from part A and 4 from part B
Let us assume the total no. of ways of answering 10 questions be N.
⇒ N = no. of ways of answering 10 questions from both parts
⇒ N = (No. of ways of answering 4 questions from part A and 6 from part B) + (No. of ways of answering 5 questions from part A and 5 questions from part B) + (No. of ways of answering 6 questions from part A and 4 from part B)
⇒ N = (6C4 × 7C6) + (6C5 × 7C5) + (6C6 × 7C4)
We know that 
,
And also n! = (n)(n – 1)......2.1
⇒ 
⇒ 
⇒ 
⇒ 
⇒ N = 105 + 126 + 35
⇒ N = 266
∴ The total no. of ways of answering 10 questions is 266 ways.
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