Question:
If n is an integer between 0 and 21, then the minimum value of $n ! (21 - n) !$ is
If n is an integer between 0 and 21, then the minimum value of $n ! (21 - n) !$ is
Updated On: Jul 6, 2022
- $9 ! 12 !$
- $10 ! 11 !$
- $20!$
- 21 !
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The Correct Option is B
Solution and Explanation
Clearly $10 \left|11\right|$ is the minimum out of the four.
$[\because\, 9\left|12\right|=9$
$\left|12\left(11\right)1>\left(9\right)\right|\left(10\right)\left(11\right)|$
$=\left(10\right)!\left(11\right)!]$
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Notes on permutations and combinations
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.