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nCr Definitions and Properties

If 19C3r = ...

Question

If $^{19} C_{3 r} =^{19} C_{r + 3}$ , then r is equal to:

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 A $4$
$^{19} C_{3 r} =^{19} C_{r + 3}$
We Know
$^{n} C_{r} =^{n} C_{n - r} \Rightarrow r + (n - r) = n \Rightarrow 3 r + r + 3 = 19 \Rightarrow 4 r = 16 \Rightarrow r = 4$
Therefore The value of $r$ is $4$

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