JEE MainMathematicsPermutations and CombinationsMCQ+4 / −1
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :
- Aat least 500 but less than 750
- Bat least 750 but less than 1000
- Cat least 1000
- Dless than 500
View written solutionFree
Correct answer: C
- Select the books
We need:
- novels from different novels
- dictionary from different dictionaries
Number of ways to choose the novels:
Number of ways to choose the dictionary:
So, total ways to select the books:
- Arrange them with the dictionary always in the middle
There are books in total. If the dictionary must always be in the middle, then its position is fixed at the place.
The remaining selected novels can be arranged in the other positions in: ways.
- Total number of arrangements
Hence, total number of required arrangements is:
- Match with options
Since it falls in:
Option C: at least 1000
- Comparison with stored correct answer
Stored correct answer: C
Our derived answer: C
So, the answer agrees with the stored correct answer.
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