# 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

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.

#### 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
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#### APPEARS IN

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