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Answer: 462</h3>
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Explanation:
Let's call the children A, B, C, D, E for the sake of simplicity. Also, let's have the children select in alphabetical order.
- Child A has 11 choices to pick from.
- Child B has 10 choices to pick from
- Child C has 9 choices to pick from
- Child D has 8 choices to pick from
- Child E has 7 choices to pick from
We started at 11 and counted down by 1 until we had all the children selecting.
Multiply out these values: 11*10*9*8*7 = 55440
There are 55440 different permutations possible. If order mattered, then we would stop here. However, order does not matter because the cereals aren't ranked and their position doesn't matter. All that matters is what fills the grocery cart. In other words, imagine the kids jumbling up the boxes as they push around the cart, so the order would be irrelevant.
Consider a group of 5 items. There are 5! = 5*4*3*2*1 = 120 different ways to arrange the five items in this group. So for any 5 cereals picked, there are 120 ways to order them. But again, order doesn't matter, so we have to correct for this over-counting. We do this by dividing by 120
55440/120 = 462
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If you want to use a formula, then plug n = 11 and r = 5 into the combination formula below and simplify.
n C r = (n!)/(r!(n-r)!)
11 C 5 = (11!)/(5!*(11-5)!)
11 C 5 = (11!)/(5!*6!)
11 C 5 = (11*10*9*8*7*6!)/(5!*6!)
11 C 5 = (11*10*9*8*7)/(5!)
11 C 5 = (11*10*9*8*7)/(5*4*3*2*1)
11 C 5 = 55440/120
11 C 5 = 462
We get the same answer.
