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How many different ways can five numbers be selected from a lottery with 33 numbers?

a) 33
b) 1035
c) 165
d) 6183

1 Answer

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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.

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