## Related questions with answers

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

In a game of musical chairs, $12$ children will sit in $11$ chairs. (1 will be left out.) How many seatings are possible?

Solution

VerifiedTo 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 $12$ children that will sit in $11$ chairs, hence there are $12$ ways to fill the first spot. Since $1$ will be left out, in the next round of a game we have $11$ children and $10$ chairs. hence, we have $11$ ways to fill the second spot. Following the same logic, in next rounds, there are $10$, $9$,...,$3$ 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 $2$ children and $1$ chair, therefore, in the last round there are $2$ possibilities. So, there are total of

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

seatings possible.

## Create an account to view solutions

## Create an account to view solutions

## More related questions

1/4

1/7