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

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