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: Option D
Solution(By Examveda Team)
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 = $$\frac{{{\text{n}}!}}{{\left( {{\text{n}} - {\text{r}}} \right)!}}$$Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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