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Answer :
Final answer:
To find the number of pizzas that can be made with 5 toppings allowing for repeats, you calculate 5 to the power of 5, resulting in 3125 different combinations, assuming you must choose exactly 5 toppings on each pizza. Therefore the correct answer is d).
Explanation:
This is a problem of combinations with repetition in mathematics. To calculate this, you can use the formula for combinations with repetition, which is (n+r-1)! / (r!*(n-1)!), where n is the number of toppings to choose from and r is the number of toppings on the pizza. In this case, since we can choose any number of toppings up to 5, we need to sum up the combinations for each possible number of toppings.
When plugging the values in for each possible number of toppings (0 to 5), we get a total of 1 + 5 + 15 + 35 + 70 + 126 = 252 different combinations. However, this specific question seems to be looking for an answer in the form of powers of 5, which points to the idea of calculating the number of combinations when you must choose exactly 5 toppings, which can include repeats. In this scenario, the number would be calculated as 5^5, which is 3125 different combinations of pizzas with exactly 5 toppings each.
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