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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,10,8,6,None of These - Mathematics

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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:
nP4 = 12 x nP2

\[\Rightarrow \frac{n!}{\left( n - 4 \right)!} = 12 \times \frac{n!}{\left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n - 2 \right)!}{\left( n - 4 \right)!} = 12\]
\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]
\[ \Rightarrow n - 2 = 4\]
\[ \Rightarrow n = 6\]
Concept: Permutations
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 13 | Page 46

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