SATHEE: Permutations and Combinations 3 Question 10

Permutations and Combinations 3 Question 10

10. Let $n$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then, the value of $\frac{m}{n}$ is

(2015 Adv.)

Show Answer

Answer:

Correct Answer: 10. (5)

Solution:

Here, $- B_{1} - B_{2} - B_{3} - B_{4} - B_{5} -$

Out of 5 girls, 4 girls are together and 1 girl is separate. Now, to select 2 positions out of 6 positions between boys $=^{6} C_{2}$

4 girls are to be selected out of $5 =^{5} C_{4}$

Now, 2 groups of girls can be arranged in 2 ! ways

Also, the group of 4 girls and 5 boys is arranged in $4! \times 5$ ! ways .

Now, total number of ways $=^{6} C_{2} \times^{5} C_{4} \times 2! \times 4! \times 5$ ! [from Eqs. (i), (ii), (iii) and (iv)]

$∴ m =^{6} C_{2} \times^{5} C_{4} \times 2! \times 4! \times 5!$

and $n = 5! \times 6$ !

$\Rightarrow \frac{m}{n} = \frac{^{6} C_{2} \times^{5} C_{4} \times 2! \times 4! \times 5!}{6! \times 5!} = \frac{15 \times 5 \times 2 \times 4!}{6 \times 5 \times 4!} = 5$

पिछला

अगला

Permutations and Combinations 3 Question 10

Answer:

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 10

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu