Answer: 70
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Explanation:
Consider we have four slots A, B, C, D.
We have 8 choices for slot A, 7 for B, 6 for C, and 5 for D.
We count down because each time we can't reuse whatever topping was picked earlier.
Multiplying out those values gives: 8*7*6*5 = 1680
There are 1680 permutations. This would be the answer if order mattered, but it doesn't matter.
Since order doesn't matter, we have to divide by 4! = 4*3*2*1 = 24. This is the number of ways to arrange any group of 4 items.
We get 1680/24 = 70 as the final answer
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Another way to get the answer is to apply the nCr combination formula
[tex]_nC_r = \frac{n!}{r!*(n-r)!}[/tex]
with n = 8 and r = 4.
Another alternative is to use Pascal's Triangle. You would look in the row that starts with 1,8,... and count out 5 slots (because r starts at r = 0) to arrive at 70.
