MCQ

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.

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#### Solution

6

According to the question:^{n}P_{4} = 12 x ^{n}P_{2}

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

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

\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]

\[ \Rightarrow n - 2 = 4\]

\[ \Rightarrow n = 6\]

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

\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]

\[ \Rightarrow n - 2 = 4\]

\[ \Rightarrow n = 6\]

Concept: Permutations

Is there an error in this question or solution?

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