If $$5{ \times ^{\text{n}}}{{\text{P}}_3} = 4{ \times ^{\left( {{\text{n}} + 1} \right)}}{{\text{P}}_{3,}}$$ find n?
a) 10
b) 11
c) 12
d) 14
Answer: d
Explanation: nP3 = n × (n–1) × (n–2)
(n+1)P3 = (n+1) × n × (n–1)
Now,
5 × n × (n–1) × (n–2) = 4 × (n+1) × n × (n–1)
Or, 5(n−2) = 4(n+1)
Or, 5n − 10 = 4n + 4
Or, 5n − 4n = 4 + 10
Hence, n = 14
Note:
nPr = $$\frac{{{\text{n}}!}}{{\left( {{\text{n}} – {\text{r}}} \right)!}}$$
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