In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B, and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B, and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is ______. [2024]

Ans.
(11376)

A B C Number of ways

5 6 4 ${}^{8}{C_{5}} \times {}^{6}{C_{6}} \times {}^{6}{C_{4}} = 56 \times 1 \times 15 = 840$

6 5 4 ${}^{8}{C_{6}} \times {}^{6}{C_{5}} \times {}^{6}{C_{4}} = 28 \times 6 \times 15 = 2520$

6 4 5 ${}^{8}{C_{6}} \times {}^{6}{C_{4}} \times {}^{6}{C_{5}} = 28 \times 15 \times 6 = 2520$

5 5 5     ${}^{8}{C_{5}} \times {}^{6}{C_{5}} \times {}^{6}{C_{5}} = 56 \times 6 \times 6 = 2016$

4 6 5     ${}^{8}{C_{4}} \times {}^{6}{C_{6}} \times {}^{6}{C_{5}} = 70 \times 1 \times 6 = 420$

4 5 6     ${}^{8}{C_{4}} \times {}^{6}{C_{5}} \times {}^{6}{C_{6}} = 70 \times 6 \times 1 = 420$

5 4 6    ${}^{8}{C_{5}} \times {}^{6}{C_{4}} \times {}^{6}{C_{6}} = 56 \times 15 \times 1 = 840$

7 4 4    ${}^{8}{C_{7}} \times {}^{6}{C_{4}} \times {}^{6}{C_{4}} = 8 \times 15 \times 15 = 1800$

$∴$   Required number of ways = 840 + 2520 + 2520 + 2016 + 420 + 420 + 840 = 11376

Want Us to Email you About Special Offers & Updates?