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 ?

Open in App

Solution

Total number of questions = 10

Question in part A = 6

Question in part B = 7

Selecting to questions with at least 4 from each part A and part B, can from done in following way.

$^{6} C_{4} \times^{7} C_{6} \times^{6} C_{5} \times^{7} C_{5} \times^{6} C_{6} \times^{7} C_{4} = (\frac{6!}{4! 2!} \times \frac{7!}{6! 1!}) + (\frac{6!}{5! 1!} \times \frac{7!}{5! 2!}) + (\frac{1 \times 7!}{4! 3!}) (∵^{n} C_{r} = \frac{n!}{r! (n - r)!}) = (\frac{6 \times 5 \times 7}{2}) + (\frac{6 \times 7 \times 6}{2} + (\frac{7 \times 6 \times 5}{3 \times 2} = (105) + (126) + 35$
266 ways

Suggest Corrections

Similar questions

Q. A student has to answer

10

questions, choosing at least

4

questions from each of parts

A

and

B

. If there are

6

questions in part

A

and

7

questions in part

B

, in how many ways can the student choose

10

questions?

Q. A question paper has two parts P and Q each containing

10

questions. If a student needs to choose

8

from part A and

4

from part B, in how many ways can he do that?

Q. A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that ?

Q. A question paper has two parts-Part A and Part B. Part A contains 5 questions and part B has 4. Each question in part A has an alternative. A student has to attempt at least one question from each part. Find the number of ways in which the student can attempt the question paper.

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 attempts 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions ?

Join BYJU'S Learning Program