Probability of girls sit together/ separated

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So, why do you say the answer is 604800? And why do you think the answer should be the same for both parts (i) and (ii)?In summary, the problem asks for the number of ways 6 boys and 4 girls can be arranged in a row. For part (i), where all girls are side by side, the solution is 120960. For part (ii), where all girls are separated by boys, the solution is 3507840. The answer of 604800 is incorrect as it does not consider all possible arrangements.
  • #1
desmond iking
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Homework Statement



Ten Students sit in a row. Find the probability of 6 boys and 4 girls can be arranged if (i) all girls are side by side?
(ii) all girls are separated by boys


Homework Equations





The Attempt at a Solution



my working for part i is 4!x7!=120960

for part ii, why can't i just take 10! -120960=3507840 ? the ans given is 604800
 
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  • #2
Part (i) looks OK to me. (7 possible positions for the first girl, 6! ways to order the boys in the remaining positions). If you take 10! minus the result of part (i), what you find is just the number of ways to not have four girls in a row. This includes e.g. gggbgbbbbb which has three girls next to each other, but the problem is asking for arrangements like gbgbbgbgbb, where no two girls are next to each other.
 
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  • #3
Your question "Find the probability of 6 boys and 4 girls can be arranged" doesn't really make sense. From what you do, it appears that the question was really "Find the number of different ways 6 boys and 4 girls can be arranged".
 

FAQ: Probability of girls sit together/ separated

What is the probability of girls sitting together in a group?

The probability of girls sitting together in a group can vary depending on the total number of girls in the group and the total number of seats available. To calculate the probability, we need to know the total number of possible seating arrangements and the number of arrangements where girls are sitting together. Then, the probability can be calculated by dividing the number of arrangements with girls sitting together by the total number of possible arrangements.

Is the probability of girls sitting together higher if there are more girls in the group?

Yes, the probability of girls sitting together is higher if there are more girls in the group. This is because the more girls there are, the higher the chance that they will be seated next to each other. However, the exact probability will also depend on the total number of seats available.

What factors can affect the probability of girls sitting together?

The probability of girls sitting together can be affected by several factors such as the total number of girls in the group, the total number of seats available, and the seating arrangement. For example, if the girls are allowed to choose their seats, the probability of them sitting together may be higher compared to a random seating arrangement.

Can the probability of girls sitting together be calculated for any group size?

Yes, the probability of girls sitting together can be calculated for any group size as long as we know the total number of girls in the group and the total number of seats available. However, for larger group sizes, the calculation may become more complex.

How can we increase the chances of girls sitting together in a group?

The chances of girls sitting together in a group can be increased by controlling the seating arrangement. For example, if we want to maximize the probability, we can seat the girls next to each other in a row or cluster them in one area. However, if we want to minimize the probability, we can seat them in a scattered or random arrangement.

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