Questions: In how many ways can 8 different pizza toppings be chosen from 25 available toppings? There are ways to choose pizza toppings.

In how many ways can 8 different pizza toppings be chosen from 25 available toppings? There are ways to choose pizza toppings.
Transcript text: In how many ways can 8 different pizza toppings be chosen from 25 available toppings? There are $\square$ ways to choose pizza toppings.
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to find the number of ways to choose \(k = 8\) items from a set of \(n = 25\) distinct items.

Step 2: Apply the Combination Formula

The formula to calculate combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\).

Step 3: Calculate Factorials

Calculate \(n!\), \(k!\), and \((n-k)!\) using the factorial function.

Step 4: Perform the Calculation

Substitute the values into the formula: \(C(25, 8) = \frac{15511210043330985984000000}{40320\times355687428096000} = 1081575\).

Final Answer:

The number of ways to choose \(k = 8\) items from a set of \(n = 25\) distinct items is 1081575.

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