A new theme park will have five roller coasters, six water rides and eight suspension rides.
If you were going to go on 5 of the 8 suspension rides, how many different ways could you do so?
I will assume that the roller coasters and the water slides are not involved, and that the order in which you go on the 5 suspension rides doesn't matter, so
you simply want 8-choose-5
= C( 8,5) = 56
To determine the number of different ways you could go on 5 of the 8 suspension rides at the theme park, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
n is the total number of items (8 suspension rides in this case)
r is the number of items you want to select (5 in this case)
! denotes factorial, which means multiplying a series of descending positive integers until 1 is reached
Now, let's calculate the number of different ways:
C(8, 5) = 8! / (5!(8-5)!)
= 8! / (5!3!)
= (8 * 7 * 6 * 5!) / (5! * 3!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 336
Therefore, there are 336 different ways you could go on 5 of the 8 suspension rides at the theme park.