The letters C, I, R, C, L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. Using these letters, how many different 6-letter strings can be formed in which the two occurrences of the letter C are separated by at least one other letter?
96
120
144
180
240
A(4,4)*C(5,2)=240
A(4,4)*C(5,2)=240
其他的四个字母A(4,4);
有5个空;
C插孔 要用C(m,n)[因为这两个字母一样不存在排列问题,用组合] C(5,2)
A(4,4)C(5,2)
先把除了C以外的字母排好 4个字母形成五个空 把2个C插入五个空有C(5,2)中排列方法
C(4,2)=6,即从4个物品当中随机抽取2个一共有6种方式。
A(4,2)表示从4个不同物品中随机抽取两个进行排列的种类。
其中A(4,2)=C(4,2)*A(2,2)=12,
A(4,4)*C(5,2)=240
A66/A22 - A55 = 240
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