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Question Number 125207 by liberty last updated on 09/Dec/20
$${Find}\:{the}\:{number}\:{of}\:{ways}\:{to}\:{choose}\:{a}\:{pair} \\ $$$$\left\{{a},{b}\right\}\:{of}\:{distinct}\:{numbers}\:{from}\:{the}\:{set}\: \\ $$$$\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{50}\right\}\:{such}\:{that}\: \\ $$$$\left({i}\right)\:\mid{a}−{b}\mid\:=\:\mathrm{5} \\ $$$$\left({ii}\right)\:\mid{a}−{b}\mid\:\leqslant\:\mathrm{5}\: \\ $$
Answered by talminator2856791 last updated on 09/Dec/20
$$\: \\ $$$$\:\left({i}\right)\:\mathrm{2}\left(\mathrm{45}\right)\:=\:\mathrm{90} \\ $$$$\left.\:\left({ii}\right)\:\mathrm{2}\left(\mathrm{5}\left(\mathrm{45}\right)+\mathrm{4}+\mathrm{3}+\mathrm{2}+\mathrm{1}\right)\right)\:=\:\mathrm{470} \\ $$
Answered by john_santu last updated on 09/Dec/20
$$\left({i}\right)\:\mathrm{45} \\ $$$$\left({ii}\right)\:\mathrm{235} \\ $$