問題の解答
検索用コード（LaTeX）
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% 例題A1.2.4：辞書式配列（One More）★★
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a，b，c，d，eの5文字を並べた文字列を，アルファベット順に，1番目をabcde，2番目をabced，$\cdots$，120番目をedcbaと番号を付ける．
(1) dbecaは何番目にあるか．
(2) 50番目の文字列は何か．
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% 例題A1.2.4の解答（One More）★★
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(1) $\mathrm{a}\square\square\square\square$の形の文字列は，$4!=24(\text{通り})$
$\mathrm{b}\square\square\square\square$の形の文字列は，$4!=24(\text{通り})$
$\mathrm{c}\square\square\square\square$の形の文字列は，$4!=24(\text{通り})$
$\mathrm{da}\square\square\square$の形の文字列は，$3!=6(\text{通り})$
$\mathrm{dba}\square\square$の形の文字列は，$2!=2(\text{通り})$
$\mathrm{dbc}\square\square$の形の文字列は，$2!=2(\text{通り})$
$\mathrm{dbeac}$の形の文字列で1通り，$\mathrm{dbeca}$の形の文字列で1通りある．
よって，$24+24+24+6+2+2+1+1=84\text{(番目)}$
(2) $\mathrm{a}\square\square\square\square$の形の文字列は，$4!=24(\text{通り})$
$\mathrm{b}\square\square\square\square$の形の文字列は，$4!=24(\text{通り})$
ここまでの合計は，$24+24=48(\text{通り})$
49番目がcabdeであるから，50番目の文字列は，cabed
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% 問題A1.2.4：辞書式配列（One More）★★
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1，2，3，4，5の5つの数字を並べてできる5桁の整数を小さい順に並べ，12345を1番目，12354を2番目，$\cdots$，54321を120番目とする．
(1) 32415は何番目にあるか．
(2) 74番目の整数は何か．
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% 問題A1.2.4の解答（One More）★★
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(1) $\mathrm{1}\square\square\square\square$の形の整数は，$4!=24(\text{通り})$
$\mathrm{2}\square\square\square\square$の形の整数は，$4!=24(\text{通り})$
$\mathrm{31}\square\square\square$の形の整数は，$3!=6(\text{通り})$
$\mathrm{321}\square\square$の形の整数は，$2!=2(\text{通り})$
$\mathrm{32415}$の形の整数で1通り
よって，$24+24+6+2+1=57\text{(番目)}$
(2) $\mathrm{1}\square\square\square\square$の形の整数は，$4!=24(\text{通り})$
$\mathrm{2}\square\square\square\square$の形の整数は，$4!=24(\text{通り})$
$\mathrm{3}\square\square\square\square$の形の整数は，$4!=24(\text{通り})$
ここまでの合計は，$24+24+24=72(\text{通り})$
73番目が41235であるから，74番目の整数は，41253
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