There are 6 runners in a race.There will be a first - place and a second - place awarded. In how many different ways can the 2 prizes be awarded.
30
The answer is 30
To determine the number of different ways the first and second place can be awarded among the 6 runners, we can use the concept of permutations.
In a permutation, the order is important. Since the first and second place awards are distinct, we need to find the number of permutations of 6 objects taken 2 at a time.
To calculate this, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects taken at a time.
In this case, we need to find P(6, 2):
P(6, 2) = 6! / (6 - 2)!
= 6! / 4!
= (6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)
= 720 / 24
= 30
Therefore, there are 30 different ways the first and second place prizes can be awarded among the 6 runners.