Ten couples founded a dance group and decided to establish a board of directors with three positions: president, secretary, and treasurer. For greater representation, it was decided that at most one person per couple could hold a position on this board.
How many different boards can be formed by these 10 couples?
(A) $10 \times 9 \times 8$
(B) $20 \times 18 \times 16$
(C) $20 \times 19 \times 18$
(D) $10 \times 9 \times 8 \times 2$
(E) $20 \times 18 \times 16 \times 2$

A music concert is divided into Part 1 and Part 2, with 2 solo teams, 2 ensemble teams, and 3 choir teams performing in total. The performance order of the 7 teams is to be determined according to the following two conditions.
(A) In Part 1, 3 teams perform in the order: solo, ensemble, choir.
(B) In Part 2, 4 teams perform in the order: solo, ensemble, choir, choir. What is the number of ways to determine the performance order for this music concert? [3 points]
(1) 18
(2) 20
(3) 22
(4) 24
(5) 26

A company employee has 6 types of tasks to handle, including tasks $\mathrm { A }$ and $\mathrm { B }$. The employee wants to handle 4 types of tasks today, including $\mathrm { A }$ and $\mathrm { B }$, and task $\mathrm { A }$ must be handled before task $\mathrm { B }$. What is the number of ways to select the tasks to handle today and determine the order of handling the selected tasks? [3 points]
(1) 60
(2) 66
(3) 72
(4) 78
(5) 84

There is a computer game where two dolls A and B are dressed in shirts and pants with undetermined colors, and then the colors of the clothes are determined. There are 3 shirts and 3 pants of different shapes, and the color of each piece of clothing is determined to be either red or green. A shirt and pants put on one doll are not put on the other doll. The colors of doll A's shirt and pants are determined to be different, and the colors of doll B's shirt and pants are also determined to be different. In this game, when dressing dolls A and B in shirts and pants and determining their colors, what is the number of possible outcomes? [4 points]
(1) 252
(2) 216
(3) 180
(4) 144
(5) 108

A company employee has 6 tasks to handle in total, including A and B. The employee wants to handle 4 tasks including A and B today, and A must be handled before B. What is the number of ways to select the tasks to handle today and determine the order of handling the selected tasks? [3 points]
(1) 60
(2) 66
(3) 72
(4) 78
(5) 84

2. In a marathon competition, the stem-and-leaf plot in Figure 1 shows the results (in minutes) of 35 athletes. [Figure]
If the athletes are numbered 1-35 according to their results from best to worst, and 7 people are selected using systematic sampling, then the number of athletes with results in the interval [139, 151] is
A. 3
B. 4
C. 5
D. 6

In a win-or-lose game, the winner gets 2 points whereas the loser gets 0. Six players A, B, C, D, E and F play each other in a preliminary round from which the top three players move to the final round. After each player has played four games, A has 6 points, B has 8 points and C has 4 points. It is also known that E won against F. In the next set of games D, E and F win their games against A, B and C respectively. If A, B and D move to the final round, the final scores of E and F are, respectively,
(A) 4 and 2
(B) 2 and 4
(C) 2 and 2
(D) 4 and 4.

The number of arrangements that can be formed from the letters $a , b , c , d , e , f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is
(1) 96
(2) 128
(3) 24
(4) 72

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
(1) At least 750 but less than 1000
(2) At least 1000
(3) Less than 500
(4) At least 500 but less than 750

We have four white cards, three red cards and three black cards. A different number is written on each of the ten cards.
(1) Choose two of the ten cards and put one in box A, and one in box B. There are $\mathbf{NO}$ ways of putting two cards in the two boxes.
(2) There are $\mathbf { P Q }$ ways of choosing two cards of the same color, and $\mathbf { R S }$ ways of choosing two cards of different colors.
Next, put the ten cards in a box and take out one card and without returning it to the box, take out second card.
(3) The probability that the two cards taken out have the same color is $\square\mathbf{ T UV}$
(4) The probability that the color of the first card taken out is white or red, and the color of the second card taken out is red or black is $\frac { \mathbf { W X } } { \mathbf { Y } \mathbf { Y } }$.

We have four white cards, three red cards and three black cards. A different number is written on each of the ten cards.
(1) Choose two of the ten cards and put one in box A, and one in box B. There are $\mathbf{NO}$ ways of putting two cards in the two boxes.
(2) There are $\mathbf { P Q }$ ways of choosing two cards of the same color, and $\mathbf { R S }$ ways of choosing two cards of different colors.
Next, put the ten cards in a box and take out one card and without returning it to the box, take out second card.
(3) The probability that the two cards taken out have the same color is $\square\mathbf{T UV}$
(4) The probability that the color of the first card taken out is white or red, and the color of the second card taken out is red or black is $\frac { \mathbf { W X } } { \mathbf { Y } \mathbf { Y } }$.

Between October 5, 2020 Monday and October 18, 2020 Sunday, including these two days, two meetings will be held on two different days within these 14 days.
If an arrangement is to be made such that at least one of the meetings is on a weekday, in how many different ways can this arrangement be made?
A) 70
B) 75
C) 80
D) 85
E) 90