SATHEE: Permutations and Combinations 3 Question 5

Permutations and Combinations 3 Question 5

5. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is

(2019 Main, 9 Jan I)

(a) 350

(b) 500

(d) 300

Show Answer

Answer:

Correct Answer: 5. (d)

Solution:

Number of girls in the class $= 5$ and number of boys in the class $= 7$

Now, total ways of forming a team of 3 boys and 2 girls

$=^{7} C_{3} \cdot^{5} C_{2} = 350$

But, if two specific boys are in team, then number of ways $=^{5} C_{1} \cdot^{5} C_{2} = 50$

Required ways, i.e. the ways in which two specific boys are not in the same team $= 350 - 50 = 300$ .

Alternate Method

Number of ways when $A$ is selected and $B$ is not

$=^{5} C_{2} \cdot^{5} C_{2} = 100$

Number of ways when $B$ is selected and $A$ is not

$=^{5} C_{2} \cdot^{5} C_{2} = 100$

Number of ways when both $A$ and $B$ are not selected

$=^{5} C_{3} \cdot^{5} C_{2} = 100$

$∴$ Required ways $= 100 + 100 + 100 = 300$ .

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Permutations and Combinations 3 Question 5

5. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is

Answer:

Alternate Method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Permutations and Combinations 3 Question 5

5. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is

Answer:

Alternate Method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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5. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is