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Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?

Sagot :

Facundo3141592idn

688,747,536 ways in which the people can take the seats.

How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?

There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.

When the whistle blows, each person needs to change to an orthogonally adjacent seat.

(This means that the person can go to the seat in front, or the seats in the sides).

This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.

Now, if we take the options that each seat has, and we take the product, we will get:

P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.

If you want to learn more about combinations:

https://brainly.com/question/11732255

#SPJ!

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