Q56 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics
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
- A$504$
- Correct answerB$336$
- C$503$
- D$335$
Solution
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 $=503-21-146=336$
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 $=503-21-146=336$
Hence, the correct answer is option: 'B'.