Answer: Choice A
20 different pizzas
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Explanation:
Consider 3 slots to fill. I'll label them slot A, B, C.
There are 6 choices for slot A, then 5 choices for B, and 4 for C. We count down by one each time since we cannot reuse a topping.
There would be 6*5*4 = 30*4 = 120 permutations if order mattered.
However, order doesn't matter with pizza toppings. So we must divide by 3*2*1 = 6 (this is the number of ways to arrange any group of 3 things)
We get 120/6 = 20 as the final answer
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Alternatively, you can use the nCr combination formula following these steps.
n C r = (n!)/(r!(n-r)!)
6 C 3 = (6!)/(3!*(6-3)!)
6 C 3 = (6!)/(3!*3!)
6 C 3 = (6*5*4*3!)/(3!*3!)
6 C 3 = (6*5*4)/(3!)
6 C 3 = (6*5*4)/(3*2*1)
6 C 3 = (120)/(6)
6 C 3 = 20 different pizzas possible
As the third to the last line shows, we have 6*5*4 up top and 3*2*1 down below. This matches exactly what was discussed in the previous section.
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Yet another alternative is to use Pascal's Triangle (see below) and we locate the row that has 1,6,... at the start. We circle the fourth item of this row that corresponds to 6C3 = 20
