A girl has to make a pizza with different toppings. There are 8 different…

Concept: When selecting a group of items where the order of selection does not matter, use combinations (nCr = n!/(r!(n−r)!)). Choosing r toppings for one pizza is a combination, not a permutation — a pizza topped with A and B is the same pizza whether A is picked first or B is picked first, so swapping the two toppings does not create a new pizza.

1. There are n = 8 toppings in total, and the girl must pick r = 2 of them for a single pizza.

2. Since the order in which the two toppings are chosen does not change the resulting pizza, this is a combination, not a permutation.

3. Apply the combination formula: 8C2 = 8!/(2! × 6!) = (8 × 7)/(2 × 1) = 28.

4. So there are 28 distinct pizzas she can make using exactly 2 different toppings out of the 8 available.

Cross-check: Try a smaller case — with 3 toppings {A, B, C}, choosing 2 gives {AB, AC, BC} = 3 pizzas, matching 3C2 = 3 (not 3P2 = 6, which would double-count AB and BA as different pizzas). The same reasoning scales up to 8C2 = 28.

Result: The correct count is 28, not 56 — 56 comes from multiplying by 2! as if the two toppings could sit in a distinguishable order on the pizza, which they cannot.