# How many different ways can runners in a race be awarded 1st 2nd and 3rd place out of 15 participants?

## How many different ways can runners in a race be awarded 1st 2nd and 3rd place out of 15 participants?

720 different
There are 720 different outcomes possible in the race.

## How many different ways can you have 1st 2nd 3rd and 4th place in a race with 6 runners?

He can occupy either 1st or 2nd or 3rd or 4th or 5th or 6th place. So, there can be 1*2*3*4*5*6 = 720 ways to finish the race.

How many different ways can 12 runners finish in the first five places of a race?

How many different ways can 12 runners finish in the first five places of a race? Since only one person can finish in first place, one in second, etc., the total number of placers is 12x11x10, or 1320 different ways the 12 racers can finish 1st, 2nd and 3rd….

How many ways can 7 runners finish a race?

The answer is 210. There are 210 different ways these seven runners could take first, second, and third place in the race.

### How many ways can 4 runners can win first second and third places?

10 • 9 • 8 = 720 possible first, second, and third place combinations.

### How many different ways can 5 students stand in a row?

Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = 120. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other.

How many ways can 8 runners in a race finish first second and third?

8 Athletes run a race and no two athletes finish exactly together. What is the number of different possible results for the first, second and third positions? I said that the answer is simply 8 choose 3, which gives an answer of 56.

How many ways can Twenty runners finish a race first second and third?

3! = 20*19*18*6 = 41040 So, out of 20 runners in a race, the first, second and third place winners can be arranged in 41040 ways.

## How many different ways can 8 runners finish a race?

8 Athletes run a race and no two athletes finish exactly together. What is the number of different possible results for the first, second and third positions? I said that the answer is simply 8 choose 3, which gives an answer of 56. When I checked the memo, it said the answer was 336.

## How many ways can 8 horses finish a race?

For our horse race situation, we would take 8 horses and place 3, like this. There are 336 ways to have 8 horses place for 1st, 2nd, and 3rd place. The work above demonstrates how one can simplify the problem using the permutation formula.

How many ways can 5 students be assigned a seat in a classroom if there are 7 seats in a row?

There are _7C5=7! 5! ⋅2! =21 ways of choosing which 5 chairs from the 7 will have people sitting in them.

How many different ways can 5 students line up to purchase a new textbook readers?

That’s 5! So, there are 120 ways to arrange five books on a bookshelf.