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Use any or all of the methods described in this section to solve the below problem.

In a game of musical chairs, 1212 children will sit in 1111 chairs. (1 will be left out.) How many seatings are possible?


Answered 1 year ago
Answered 1 year ago
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To solve this problem we can use few methods.

Let's solve it using the fundamental principle of counting, as follows:

At the beginig, in a game of musical chairs there are total of 1212 children that will sit in 1111 chairs, hence there are 1212 ways to fill the first spot. Since 11 will be left out, in the next round of a game we have 1111 children and 1010 chairs. hence, we have 1111 ways to fill the second spot. Following the same logic, in next rounds, there are 1010, 99,...,33 ways to fill the tenth, nineth,...,third spot.As the games continous, there will be less children and less chairs, until the last round in which will be 22 children and 11 chair, therefore, in the last round there are 22 possibilities. So, there are total of

121110321=12!\begin{aligned} 12\cdot11\cdot10\cdots3\cdot2\cdot1=12! \end{aligned}

seatings possible.

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