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# counting problem

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Two boys and three girls are going to sit around a table with 5 different chairs. If the two boys want to sit next to Jill, in how many possible ways can they be seated?

Jun 20, 2021

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Let the two boys and Jill be one: There are $\binom{3}{2} = 3$ possibilities to permute them.

Then there are $5-3 + 1 = 3$ people. There is $\binom{5}{3} = 10.$

the answer is $10\cdot 3 = \boxed{30}$

Jun 20, 2021