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数学 中学生

 確率 塾技解説…のマーカーで引いた部分の4はどこから出てきたのか教えてください

塾技 33 場合の数・確率 ② 順列 異なるn個のものから、 異なるr個を選んで並べる並べ方を順列 (permutation)といい „Pで表す。 „P,=nx(n-1)x(n-2)x...×(n-r+1) 個の積 組み合わせ 異なるn個のものから、 異なるr個を選ぶ選び方を組み合わせ (combination)といい n C で表す。 塾技 解説 „C₁ = P² Pr nx(n-1)x(n-2)x...x(n-r+1) rx(r-1)x...×2×1 = 場合の数・確率の問題には ① 選んで並べる問題(順列の問題という), ②選ぶだけで, 並べる順序は関係ない問題 (組み合わせの問題という)の2つのパターンがある けた ①の例 ① 1 2 3 4 5 の5枚のカードから3枚選んで3桁の整数を作る。 何通りの整数が作れますか。 この例は,3枚選んで、順に百の位・十の位一の位と並べるので順列!よって, P3=5×4×3=60 (通り) GALER ②の例 A,B,C,D,E の5人から3人を選んでグループを作る。 何通りのグループが作れますか。 この例は,5人から3人選ぶだけなので組み合わせ よって, 12 = =10 (通り) 3×2×1 5P3 (5人から3人を選んで順に並べる並べ方)5×4×3 5Cg= 3P3 (選んだ3人の並べ方) 3P 3 で割る理由は,重複があるから。 例えば A,B,Cの3人を選んで並べる並べ方は, (A,B,C), (A, C, B), (B, A, C), (B,C, A), (C, A, B), (C, B, A) の6通り あるけど, グループとして考えたらどれも同じ3人だよね。 だから、 異なる3人を並べ る並べ方 (3P3) で割るというわけなんだ。 入試 問題1 るか 「解」 両端 男

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英語 高校生

空欄にはbが入るのですが、その理由を教えていただけませんか?

次の英文を読み, 後の問いに答えよ。 oh ni ai tuned" goizer o d Beauty is in the eye of the beholder. 1 This proverb was first recorded in the English language in its current form in the 19th century. However, (1). the concept of people viewing beauty differently from their own points of view has been around in most cultures of the world since ancient times. But what exactly is beauty, and is it really subjective? The definition in the Merriam-Webster dictionary is "the qualities in a person or a thing that give pleasure to the senses or the mind." This definition, however, does not mention whether there is a universal standard for beauty, or whether each individual person views beauty based on a totally different set of standards. Some of the arts seem to suggest the (2) if we consider the fact that everybody has their own favorite piece of music or painting that they consider to be beautiful. Nature, on the other hand, consistently comes up with scenes that are universally considered to be beautiful. There is little doubt that physical beauty, or beauty based on physical appearance of people, is personal. The ideal "beautiful woman" differs between cultures, and in many cases is based on fashion. Some cultures appreciate fatness, while others believe that body mutilation 2 represents beau example, body art in the form of piercings and tattoos is recognized as a sign of beauty in many countries of the world today, although there are also many people in these same countries who continue to ( 4 ) with this assessment. (3). For hana including Pythagoras believed that beauty was based on 1:1 11

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