平成23年度秋期 ITパスポート試験問37

This question's explanation and your answers so far.

問37

頻出度★★☆

インタフェースを一つだけもつモジュールが 6 個ある。これらのモジュールが相互に結合できるかを試験したい。1 組のモジュールの結合テストに 4 時間を要するとき, 全ての組合せのテストに合計何時間掛かるか。

出典　平成23年度秋期 ITパスポート試験問37

解説

問 37

Incorrectア
20 is the value obtained by counting only 5 pairs and computing 5×4 = 20. It corresponds to the number of adjacent connections when the 6 modules are lined up in a row (n−1 = 5), and it does not satisfy the condition of testing them “mutually”, that is, in every combination of 2. There are 15 combinations in all, so this is wrong.
Incorrectイ
24 comes from 6×4 = 24, that is, assuming one test per single module. An integration test is carried out per “pair (2 modules)”, so what must be counted is not the number of modules but the number of pairs, 15. This choice is therefore wrong.
ウ
正解 Each module has only one interface, so the integration test is run once for every combination that pairs 2 modules into one set. The total number of ways to choose 2 out of 6 is C(6,2) = (6×5)÷(2×1) = 15. Each pair takes 4 hours, so the total is 15 × 4 = 60 hours. Therefore “ウ (60)” is correct. Order does not matter (the pair A and B is the same test as the pair B and A), so the key point is to count with combinations, not permutations.
Incorrectエ
120 is the value from treating the count as the permutation 6P2 = 6×5 = 30 pairs and computing 30×4 = 120. The integration test of A with B and that of B with A are the same test, so distinguishing the order counts each one twice and overstates the total. Correctly, dividing by 2 gives C(6,2) = 15 pairs and 60 hours.

ここがポイント

Total number of combinations: choosing 2 out of n gives C(n,2) = n(n−1)÷2. Here C(6,2) = 15 pairs. Do not confuse this with the permutation that distinguishes order (nP2 = n(n−1)).
Effort estimation for integration testing: total effort = number of combinations × time required per pair. Keep in mind that as the number of modules grows, the number of combinations rises sharply (on the order of n²).

用語

解答問37ウ