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# Counting

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Cory has 3 apples, 2 oranges and $$3$$ bananas. If Cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can Cory eat the fruit? One such order is $$AAAOOBBB$$

Jan 23, 2022

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There would be 8 options for the first day, 7 for the second, 6 for the third, and so on... So 8x7x6x5x4x3x2. However, since the fruits are indistinguishable, we have to divide by 3!x2!x2!.

This gives us: $${{8*7*6*5*4*3*2} \over 3!2!2! } = 420$$ ways.

Jan 24, 2022