Find n if n-1P3: nP3 = 1: 9.
Solution and Explanation
n-1P3: nP3 = 1: 9
\(⇒\frac{^{n-1}P_3}{^nP_3} = \frac{1}{ 9}\)
\(⇒\frac{\left[\frac{(n-1)!}{(n-1-3)!}\right]}{\left[\frac{n!}{(n-4)!}\right]}=\frac{1}{9}\)
\(⇒\frac{(n-1)!}{(n-4)!}\times\frac{(n-4)!}{n!}=\frac{1}{9}\)
\(⇒\frac{(n-1)!}{n\times(n-1)!}=\frac{1}{9}\)
\(⇒\frac{1}{n}=\frac{1}{9}\)
\(∴n=9\)
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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.