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排列組合   題數(shù)：8
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?(1) The number of distinct points in S is 5.(2) No three of the points in S are collinear.
On her way home from work, Janet drives through several tollbooths. Is there a pair of these tollbooths that are less than 10 miles apart? (1) The first tollbooth and the last tollbooth are 25 miles apart. (2) Janet drives through 4 tollbooths on her way home from work.
Are there exactly 3 distinct symbols used 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 horizontal arrangements of one or more symbols, with no repetition.(2) There are exactly 15 code words in language Q.
A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is the value of n?(1) The probability that the two bulbs to be drawn will be defective is 1/15.(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.
Of the 25 cars sold at a certain dealership yesterday, some had automatic transmission and some had antilock brakes. How many of the cars had automatic transmission but not antilock brakes? (1) All of the cars that had antilock brakes also had automatic transmission. (2) 2 of the cars had neither automatic transmission nor antilock brakes.
If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2 ?(1) More than 1/2 of the 10 employees are women.(2) The probability that both representatives selected will be men is less than 1/10.
【OG20-P291-428題】Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each rowand exactly once in each column. What is the value of r ?(1) v + z = 6(2) s+t + u + x = 6
If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?(1) More than 1/2 of the 10 employees are women.(2) The probability that both representatives selected will be men is less than 1/10 .
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