排列组合-PS-OG：第1-12题 练习册详情

1

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

• 4
• 5
• 6
• 7
• 8

10000人做过此题 平均耗时为6min8s 平均正确率为 59%

展开题目内容

2

A = {2, 3, 4, 5)

B = {4, 5, 6, 7,8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9?

• 0.15
• 0.20
• 0.25
• 0.30
• 0.33

1984人做过此题 平均耗时为1min37s 平均正确率为 84%

展开题目内容

3

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

• 15
• 16
• 28
• 56
• 64

7104人做过此题 平均耗时为21min51s 平均正确率为 45%

展开题目内容

4

The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

• 6
• 7
• 12
• 14
• 17

5154人做过此题 平均耗时为14min40s 平均正确率为 61%

展开题目内容

5

A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by

• $$\frac{w}{m}$$
• $$\frac{w}{w+m}$$
• $$\frac{w+3}{m+2}$$
• $$\frac{w+3}{w+m+3}$$
• $$\frac{w+3}{w+m+5}$$

9992人做过此题 平均耗时为4min7s 平均正确率为 50%

展开题目内容

6

The probability is $$\frac{1}{2}$$ that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

• $$\frac{1}{8}$$
• $$\frac{1}{2}$$
• $$\frac{3}{4}$$
• $$\frac{7}{8}$$
• $$\frac{15}{16}$$

1473人做过此题 平均耗时为1min28s 平均正确率为 73%

展开题目内容

7

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?

• 6
• 8
• 10
• 14
• 16

1645人做过此题 平均耗时为2min37s 平均正确率为 41%

展开题目内容

8

Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

• $$\frac{2}{5}$$
• $$\frac{2}{7}$$
• $$\frac{33}{83}$$
• $$\frac{99}{250}$$
• $$\frac{100}{249}$$

9978人做过此题 平均耗时为7min52s 平均正确率为 69%

展开题目内容

9

A three-digit code for certain logs uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

• 144
• 152
• 160
• 168
• 176

7863人做过此题 平均耗时为25min32s 平均正确率为 45%

展开题目内容

10

The letters D, G, I, I, and T can be used to form 5-letter strings such as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by least one other letter?

• 12
• 18
• 24
• 36
• 48

1309人做过此题 平均耗时为14min32s 平均正确率为 46%

展开题目内容

11

Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to line up male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

• 9
• 12
• 15
• 36
• 720

3029人做过此题 平均耗时为17min1s 平均正确率为 62%

展开题目内容

12

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

• 6
• 40
• 210
• 5,040
• 151,200

1151人做过此题 平均耗时为7min30s 平均正确率为 57%

展开题目内容