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Number of Functions Possible from Set A to Set B

Set of values...

Question

Set of values of r for which $^{18} C_{r - 2} + 2 \cdot^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$ contains

A

4

elements

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B

5

elements

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C

7

elements

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D

10

elements

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Solution

The correct option is A $7$ elements
Simplifying LHS we get

$^{18} C_{r - 2} +^{18} C_{r - 1} +^{18} C_{r - 1} +^{18} C_{r}$

$=^{19} C_{r - 1} +^{19} C_{r}$

$=^{20} C_{r}$

$\geq^{20} C_{13}$

Hence
$^{20} C_{r} \geq^{20} C_{7}$
Hence
$r \in {7, 8, 9, 10, 11, 12, 13}$

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