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A student has to answer 10 questions choosing at least 4 from each of part A and B. If there are 6 questions in part A and 7 in part B then in how many ways can a student choose 10 questions? i know the usual approach to solve this question by making cases.. i want to know what am i doing wrong in this 6C4 x 7C4 x 5C2 first i did 4 ques from 6 of part A den 4 of 7 from B and den 2 from any remaining 5??

A student has to answer 10 questions choosing at least 4 from each of part A and B. If there are 6 questions in part A and 7 in part B then in how many ways can a student choose 10 questions?

i know the usual approach to solve this question by making cases.. i want to know what am i doing wrong in this

6C4 x 7C4 x 5C2
first i did 4 ques from 6 of part A den 4 of 7 from B and den 2 from any remaining 5??

Grade:12

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
see make 3 cases , in this way this problem becomes much simpler,
part A : 4 and part B : 6
part A : 5 and part B : 5
part A : 6 and part B : 4

sher mohammad
b.tech, iit delhi
Akshay
11 Points
5 years ago
The question makes 3 cases...1) When 4 questions are chosen from A and rest 6 from B2) When 5 questions are chosen from A and rest 5 from B3) When 6 questions are chosen from A and rest 4 from BThis makes the answer...(6C4×7C6) + (6C5×7C5) + ( 6C4× 7C6)This makes the answer...105+126+35= 266 ways

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