Final answer:
The number of different ways that five numbers can be selected from a lottery with 33 numbers is 33,649.
Step-by-step explanation:
The number of different ways that five numbers can be selected from a lottery with 33 numbers is calculated using the concept of combinations. The formula for calculating combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of options available and r is the number of options being selected. In this case, n=33 (the total number of numbers in the lottery) and r=5 (the number of numbers being selected). Plugging in these values into the formula, we get:
C(33, 5) = 33! / (5!(33-5)!)
Calculating this expression gives us:
C(33, 5) = 33! / (5! * 28!)
Since calculating factorials can be time-consuming, we can use a calculator or a math software to simplify this expression to:
C(33, 5) = 33 * 32 * 31 * 30 * 29 / (5 * 4 * 3 * 2 * 1)
Simplifying further, we get:
C(33, 5) = 33 * 32 * 31 * 30 * 29 / 5 * 4 * 3 * 2 * 1
Calculating this expression gives us a total of 33,649 different ways that five numbers can be selected from a lottery with 33 numbers.