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Permutation and Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutation and Combinations1 Mark
Question
State True or False for the following statement:

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.

✓

Answer

False.
Solution:
A candidate can attempt questions in following maimer
Group A
2
3
4
5
Group B
5
4
3
2
 So, the Number of attempts of 7 question
$=\ ^6\text{C}_2\times\ ^6\text{C}_5+\ 6\text{C}_3\times\ ^6\text{C}_4+\ ^6\text{C}_4+\ ^6\text{C}_3+\ ^6\text{C}_5\times\ ^6\text{C}_2$
$=2[\ ^6\text{C}_2\times\ ^6\text{C}_5+\ ^6\text{C}_3\times\ ^6\text{C}_4$
$=2[15\times6+20\times15]=2[90+300]=2\times390=780$

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