Question

If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

Options

• 10

• 8

• 6

• none of these.

Answer 1

6
According to the question:
ⁿP₄ = 12 x ⁿP₂

\[\Rightarrow \frac{n!}{\left( n - 4 \right)!} = 12 \times \frac{n!}{\left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n - 2 \right)!}{\left( n - 4 \right)!} = 12\]
\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]
\[ \Rightarrow n - 2 = 4\]
\[ \Rightarrow n = 6\]