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nCr Definitions and Properties

If 10 C r =...

Question

If $^{10} C_{r} = 120$ , find the value of r

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Solution

$^{10} C_{r} = 120 \Rightarrow \frac{10!}{120} = (10 - r)! r!$
$\Rightarrow (10 - r) r! = 30.240 = 7! 3! \Rightarrow r = 3$

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^{n} P_{r} = 720

^{n} C_{r} = 120

, then what is the value of 'r'.

{^{n} P}_{r} = 720

{^{n} C}_{r} = 120

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