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Question Number 183424 by Shrinava last updated on 25/Dec/22

Among the natural numbers not  greater than 22 , the probability that  the modulus of the difference of any   two of the 3 randomly selected numbers  is greater than 5 is equal to which of  the following?  a)15/22   b)1/7   c)1/22   d)1

$$\mathrm{Among}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{not} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{22}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{randomly}\:\mathrm{selected}\:\mathrm{numbers} \\ $$$$\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}/\mathrm{22}\:\:\:\mathrm{b}\right)\mathrm{1}/\mathrm{7}\:\:\:\mathrm{c}\right)\mathrm{1}/\mathrm{22}\:\:\:\mathrm{d}\right)\mathrm{1} \\ $$

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