How many ways can 5 students be seated in a row?

So there are 120 different ways to seat 5 girls in 5 chairs.

How many different ways can five students be seated in three chairs?

There are (53)=10 ways of picking 3 seats from 5, and there are 3! =6 ways to assign the kids to those 3 seats once you’ve picked them. So using the multiplication principle, there are 10⋅6=60 ways to assign the kids to seats.

How many ways can 5 persons occupy 3 seats?

Therefore, the number of possible solutions is 60.

How many ways can 3 students be assigned a seat in a classroom if there are 5 seats in a row?

How many ways can 3 people sit in 3 chairs?

So there are two answers: There are 3! = 6 different ways of placing these three people in three distinct chairs. However, it we decide to consider rotated arrangements as basically the same, then there are only 2 ways.

How many chairs do I need for 3 people?

You’re essentially choosing three of the five chairs, and then imposing an order on those three chairs corresponding to the three people. So yes, 5 P 3 is correct. 60 sounds good assuming that they must all be seated.

How many vacant chairs could be distributed among 10 people?

The first is the number of ways the 6 people could be arranged, without considering the vacant chairs. The second is the number of ways 4 vacant chairs could be distributed among 10, meaning the other 6 were occupied. Then multiply the 2 results.

How many ways can you seat 7 people in a room?

In a straight line (i.e. seating seven people in seven chairs next to each other), there are clearly 7! ways. But when they are joined in a circle, a rotation still counts the same way of seating everyone.

How many ways can 6 people sit around a circular table?

Now the remaining seats differ since a new person may sit to the right or left (clockwise/anticlockwise) of the first person, therefore there are 6! ways for 6 people to be situated around the table (with one place already taken by the first person). Therefore there are 1 × 6! ways for people to sit around a circular table.