If there are 6 alike fruits, 7 alike vegetables and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is

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Aicharya · Accepted Answer

Total number of ways of selecting one or more things $=(6+1)(7+1)(8+1)-1=503$
Now, total ways to select from only one category $=6+7+8=21$
Total ways to select from only two category $=6 \times 7+8 \times 6+7 \times 8=146$
So, required total ways of selecting at least one or more things from each category $=503-21-146=336$

If there are 6 alike fruits, 7 alike vegetables and 8 alike biscuits, then the number of ways of selecting…

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