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  3. The number of connections C that can be made through a switchboard to which T telephones are connected is given by the formula C

The number of connections C that can be made through a switchboard to which T telephones are connected is given by the formula C

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问题 The number of connections C that can be made through a switchboard to which T telephones are connected is given by the formula C = T(T-1)/2. How many more connections are possible with 30 telephones than with 20 telephones?
选项 A、435
B、245
C、190
D、45
E、10
答案B
解析 连接有T门电话的交换机所能形成的连络数目C由公式C=T(t-1)/2给定。30门电话能比20门电话多出多少连络?
解：本题的正确答案是(B)。30门电话的连络数目：C(30)=30×(30-1)/2=435；20门电话的连络数目：C(20)=20×(20-1)=190；C(30)-C(20)=435-190=245
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