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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.
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Solution
6
According to the question:
nP4 = 12 x nP2
\[ \Rightarrow \frac{\left( n - 2 \right)!}{\left( n - 4 \right)!} = 12\]
\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]
\[ \Rightarrow n - 2 = 4\]
\[ \Rightarrow n = 6\]
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