Five toppings for a pizza are available at Polina's Pizza. How many combinations of two different toppings are possible?
I need to count the number of ways to choose two toppings out of five, without regard to the order of the toppings. This is a combination problem, not a permutation problem, because the order of the toppings does not matter. I recall that the formula for the number of combinations of n objects taken r at a time is nCr = n!/(r!(n-r)!), where n! is the factorial of n, meaning the product of all positive integers up to n. In this case, n = 5 and r = 2, so I plug those values into the formula: 5C2 = 5!/(2!(5-2)!) I simplify the expression by canceling out some factors: 5C2 = (5*4*3*2*1)/(2*1*3*2*1) = (5*4)/(2*1) = 10 Therefore, there are 10 combinations of two different toppings for a pizza. 