問42
頻出度★★☆
1対1で情報の伝達を行う必要があるプロジェクトチームにおいて，メンバが6人から10人に増えた場合，情報の伝達を行うために必要な経路の数は何倍になるか。
平成30年度 秋期 ITパスポート試験 問42
テクノロジ系基礎理論 › 応用数学
This question's explanation and your answers so far.
解説
問 42
Incorrectア
“1.5” is neither the ratio of people 10÷6≈1.67 nor the ratio of paths, but a half-baked value. Because the number of paths does not grow in proportion to the number of people but grows as combinations, estimating the increase in paths as 1.5 times when the number of people rises about 1.67 times is wrong.
Incorrectイ
“2.5” does not match the factor of 3 obtained from the correct path counts (15 paths → 45 paths). If C(6,2)=15 and C(10,2)=45 are calculated correctly, the result is not 2.5.
- ウ
正解 The number of paths for one-to-one communication equals the number of combinations of choosing 2 people from the members: C(n,2)=n×(n−1)÷2. For 6 people this is 6×5÷2=15 paths, and for 10 people it is 10×9÷2=45 paths. Therefore the number of paths increases by a factor of 45÷15=3. So the correct answer is choice “ウ”, 3.
Incorrectエ
“6” is an overly large value that mistakes the path counts themselves (45 paths for 10 people, 15 paths for 6 people) or the factor of 3 for something like the ratio of people. The actual factor is 45÷15=3, not 6.
ここがポイント
- When n people communicate one-to-one, the number of paths is found by the combination C(n,2)=n×(n−1)÷2 (the total number of lines connecting every pair of people with one line each).
- The number of paths does not simply scale with the number of people but increases sharply as the number of people grows. The factor is obtained by first computing C(n,2) for each number of people and then dividing.
用語