If there are 50 floats in a parade, how many ways can a first place and a second place trophy be awarded?
what is 50x49 ?
To determine the number of ways a first place and a second place trophy can be awarded in a parade with 50 floats, you can follow these steps:
Step 1: Calculate the number of possibilities for the first place trophy.
Since there are 50 floats participating, any of the 50 floats can be awarded the first place trophy. Therefore, there are 50 options for the first place trophy.
Step 2: Calculate the number of possibilities for the second place trophy.
After the first place trophy is awarded, there are now 49 remaining options for the second place trophy. Any of these 49 floats can be awarded the second place trophy.
Step 3: Multiply the number of possibilities for the first place trophy by the number of possibilities for the second place trophy.
To find the total number of ways the first and second place trophies can be awarded, multiply the number of possibilities for the first place trophy by the number of possibilities for the second place trophy.
50 (options for first place trophy) * 49 (options for second place trophy) = 2450
Therefore, there are 2450 ways the first place and second place trophies can be awarded in the parade.
To determine the number of ways a first place and a second place trophy can be awarded among 50 floats, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we need to find two different arrangements: one for the first place trophy and another for the second place trophy. Since the order matters, we will use permutations.
To calculate the number of permutations, we use the formula for permutations of n objects taken r at a time:
P(n, r) = n! / (n-r)!
Where:
- n is the total number of objects
- r is the number of objects taken at a time
- ! denotes the factorial operation (e.g., 5! = 5 x 4 x 3 x 2 x 1)
In our case, n = 50 (the number of floats) and r = 2 (the number of trophies to be awarded). Substituting these values into the formula:
P(50, 2) = 50! / (50-2)!
P(50, 2) = 50! / 48!
Calculating the factorial value, we get:
P(50, 2) = (50 x 49 x 48!) / 48!
Simplifying further:
P(50, 2) = 50 x 49
P(50, 2) = 2,450
Therefore, there are 2,450 ways that a first place and a second place trophy can be awarded among 50 floats in the parade.