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Expert: Robi Bhattacharjee - 9/24/2008


Question
Suppose you have members of six families which each consist of a mom, a dad, and a kid.

How many ways can the families sit in a row of 18 chairs such that the members of each family are sitting together.  

I realize that there are six possible arrangements of the the three family members which must sit together.  What is confusing me is regarding how to deal with the situation of the chairs.

Thank you so much for you help!

Answer
Hello Jolene,

So, you have 18 people in six families and you have 18 chairs.  You want the members of each family to sit together, so the number of ways to do that is going to be 6! because you treat each group of three chairs as a  single one because each family will take up one group of three chairs in a row.  So, the answer is (# of ways to arrange the families) * (# of ways each family can be organized), which is 6! * 3! = 720 *6 = 4320.

Hope that answered your question,


Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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