1). Are there exactly 3 distinctly symbols ued to create the code words in language Q?
(1). The set of all code words in language Q is the set of all possible distinct horizonal arrangements of one or more symbols, with no repetition.
(2). There are exactly 15 code words in language Q.
2). Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length？
A. six
B. eight
C. ten
D. fourteen
E. sixteen
3). In the figure above, two searchlights S1 and S2 are located 10000 feet apart, each covers an area of radius 10000 feet, and each is located 8000 feet from the railroad track. To the nearest 1000 feet, what is the total length X of track spanned by the searchlights?
A. 24000
B. 22000
C. 20000
D. 16000
E. 12000
4). Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips, and 5 green chips. If all of these chips are used and each stack contains at least one chip of each color, what is the maximum number of red chips in anyone stack?
A.7
B.6
C.5
D.4
E.3
5). Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure than 80 of the books removed are on the same science?
A.81
B.159
C.166
D.285
E.324
不知道答案,我试试看我的解答
1.选B.(1)里面说set里面是所有1个或1个以上不同符号的arrangement,那有无数个吧...
(2)里面说Q只有15个code word,那么用3个symbol正好可以表示,p(3,1)+p(3,2)+p(3,3)=15
2,3题都要看图的......
4.选C.每个stack一共要有7个chip,因为每个stack至少要每个颜色一个,所以先分配1R1B1G给每个stack, 这样剩下6R,4B,2G.所以拿到R最多的stack就是剩下4个全是R,总共5个.
5. 选E.因为只有物理和化学有超过80本的书,其它都不超过80本.所以要让最后肯定有80本一样的书,那么最糟糕的情况就是拿走的书里面含有所有其他的3种书,也就是50+65+50.那么剩下的90本物理110本化学,最好的拿法是正好拿了80本物理或80本数学.最郁闷的当然是拿了一种79本,另一种80本.所以答案是50+65+50+80+79=324.
第2题没图，第3题我图画不好。。。
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