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4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is
- a)1/2
- b)1/4
- c)1/3
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
4 boys and 2 girls occupy seats in a row at random. Then the probabili...
Understanding the Problem
To find the probability that the two girls occupy seats side by side when seated with four boys, we can use combinatorial methods.
Total Arrangements
- The total number of ways to arrange 6 individuals (4 boys and 2 girls) in a row is calculated as follows:
- Total arrangements = 6! = 720
Group the Girls
- To find the arrangements where the two girls are sitting next to each other, we can treat them as a single unit or block.
- This block, combined with the four boys, gives us 5 units to arrange (4 boys + 1 girl block).
- The arrangements of these 5 units is:
- Arrangements = 5! = 120
- Inside the girl block, the two girls can be arranged among themselves in:
- Arrangements = 2! = 2
- Therefore, the total arrangements with the girls together is:
- Total = 5! * 2! = 120 * 2 = 240
Calculating the Probability
- Now, we calculate the probability that the two girls are sitting side by side:
- Probability = (Arrangements with girls together) / (Total arrangements)
- Probability = 240 / 720 = 1/3
Conclusion
- The probability that the two girls occupy seats side by side is 1/3.
Thus, the correct answer is option 'C'.
To find the probability that the two girls occupy seats side by side when seated with four boys, we can use combinatorial methods.
Total Arrangements
- The total number of ways to arrange 6 individuals (4 boys and 2 girls) in a row is calculated as follows:
- Total arrangements = 6! = 720
Group the Girls
- To find the arrangements where the two girls are sitting next to each other, we can treat them as a single unit or block.
- This block, combined with the four boys, gives us 5 units to arrange (4 boys + 1 girl block).
- The arrangements of these 5 units is:
- Arrangements = 5! = 120
- Inside the girl block, the two girls can be arranged among themselves in:
- Arrangements = 2! = 2
- Therefore, the total arrangements with the girls together is:
- Total = 5! * 2! = 120 * 2 = 240
Calculating the Probability
- Now, we calculate the probability that the two girls are sitting side by side:
- Probability = (Arrangements with girls together) / (Total arrangements)
- Probability = 240 / 720 = 1/3
Conclusion
- The probability that the two girls occupy seats side by side is 1/3.
Thus, the correct answer is option 'C'.
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Community Answer
4 boys and 2 girls occupy seats in a row at random. Then the probabili...
5!*2/6! = 1/3
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