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nCr Definitions and Properties

If nPr= 360...

Question

If $^{n} P_{r} = 360$ and $^{n} C_{r} = 15$ then find the value of r

A

5

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B

4

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C

3

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D

2

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Solution

The correct option is D $4$
$^{n} P_{r} = \frac{n!}{(n - r)!} = 360$ -- (1)
$^{n} C_{r} = \frac{n!}{(r!) (n - r)!} = 15$ -- (2)
Dividing eqn 1 by 2, we get
$=> r! = \frac{360}{15} = 24$
$=> r! = 4 \times 2 \times 3 \times 1 = 4!$
So, $r = 4$

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