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Probability

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by s91arvindh » Sat Apr 19, 2014 5:28 am
5 boys and 5 girls (5 pairs of brother and sister) are arranged randomly in a row. What is the probability
  • all boys are together
    all boys and all girls are together
    all siblings are together
    all siblings are not together
I am trying to solve the above questions but stuck somewhere .[/list]
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by [email protected] » Sat Apr 19, 2014 3:14 pm
Hi s91arvindh,

As a general rule, you should submit just 1 question per post. This will minimize the number of sub-conversations that might occur around any one question.

Did these questions come from a GMAT Course/Book or are they from a math class? If they're from a GMAT Source, then you should include the 5 answers for reference.

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by s91arvindh » Sun Apr 20, 2014 3:34 am
Sorry for the trouble!!

These are questions are from my Math class.

5 boys and 5 girls (5 pairs of brother and sister) are arranged randomly in a row. What is the probability

How to find all siblings are together

PS:No Answer is provided

Thanks
Arvindh
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by Matt@VeritasPrep » Mon Apr 21, 2014 10:01 am
Hey, it's a good question - let me take a shot at it.

The probability of any event can be expressed as

# of Target Outcomes
--------------------
# of Total Outcomes

Since we're arranging 10 people in a row, the number of total outcomes is 10!.

If you want to have five sets of siblings together, the easiest way to start is to force them into five pairs, then to arrange those five pairs. Five pairs can be arranged in 5! different ways, so we start there. Then, each pair could be arranged in two ways (brother left, sister right, or vice versa), so we multiply that by 2�.

All in all, we get (2� * 5!)/10!
s91arvindh wrote:Sorry for the trouble!!

These are questions are from my Math class.

5 boys and 5 girls (5 pairs of brother and sister) are arranged randomly in a row. What is the probability

How to find all siblings are together

PS:No Answer is provided

Thanks
Arvindh
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Posts: 2630
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by Matt@VeritasPrep » Mon Apr 21, 2014 10:06 am
s91arvindh wrote:5 boys and 5 girls (5 pairs of brother and sister) are arranged randomly in a row. What is the probability
  • all boys are together
    all boys and all girls are together
    all siblings are together
    all siblings are not together
I am trying to solve the above questions but stuck somewhere .[/list]
Here are some quick answers for the others:

1:: All the boys together.

Treat the five boys as ONE person, and each of the girls as ONE person. That means we have 6 "people" to arrange, which gives us 6!. Then, the five boys must be arranged amongst themselves, so that gives us another 5! possible arrangements, so we have 6! * 5!. (If it's a probability question, make sure the denominator is 10!)

2:: All the boys together and all the girls together.

Treat the five boys as ONE person, then the five girls as ONE person. That means we have two "people" to arrange, or 2!. Then, we have the arrange the boys amongst themselves (5!) and the girls amongst themselves (5!), so we have 2! * 5! * 5!. (If it's a probability question, make sure the denominator is 10!)

3:: All the siblings together.

I did this one in my last post (above).

4:: All the siblings NOT together.

Not quite sure I understand this. Is this NO sibling sitting next to his or her sibling, or is this AT LEAST ONE sibling not sitting next to his or her sibling?
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