A new theme park will have five roller coasters, six water rides and eight suspension rides. How many different combinations of rides could you try at this park.
5 * 6 * 8 = ?
240
To calculate the total number of different combinations of rides you could try at this park, you can use the formula for finding the combinations of objects when order does not matter.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where "n" represents the total number of different types of rides available and "r" represents the number of rides you can choose at a time.
In this case, we have:
n = 5 (roller coasters) + 6 (water rides) + 8 (suspension rides) = 19
r = total number of rides you want to try
Since the problem does not specify a specific number of rides to try, we will assume that the total number of rides you can choose at a time can vary from 0 to 19 (trying all possible combinations).
So, we need to calculate the sum of all the combinations for r = 0 to 19.
Total combinations = C(19,0) + C(19,1) + C(19,2) + ... + C(19,19)
To calculate this sum, we can use the shortcut formula:
Total combinations = 2^n - 1
where "n" is the number of elements.
Applying this formula to our problem:
Total combinations = 2^19 - 1 = 524,287
Therefore, you could try a total of 524,287 different combinations of rides at this theme park.
To find the number of different combinations of rides that you could try at this park, you can use the concept of counting principle and combinatorics.
The counting principle states that if there are m ways to do one thing, and n ways to do another thing, then there are m * n ways to do both things. In other words, you multiply the number of options for each choice to find the total number of combinations.
In this case, there are five roller coasters, six water rides, and eight suspension rides.
You have the option to choose one roller coaster from the five available options. And for each of the roller coasters, you have six options of water rides. Therefore, the total number of combinations for the roller coaster and water ride choices is 5 * 6 = 30.
Now, for each of these 30 combinations, you have eight options for suspension rides. Therefore, to find the total number of combinations of all three ride types, you multiply the previous result (30) by 8.
Thus, the total number of different combinations of rides you could try at this park is 30 * 8 = 240.