a、8 1 B、64 C、 12 D、 14

2, n∈N and n

A, B, C, D,

3. Four numbers (1, 2, 3, 4) can be used to form the number () of natural numbers whose numbers are not repeated.

a、64 B、60 C、24 D、256

4. Three different movie tickets are distributed to 10 people, and each person has at most one ticket, so the number of different kinds of tickets is ().

a、2 160 B、 120 C、240 D、720

5. Arrange a program list with five solos and three choruses. If the chorus program cannot be ranked first and the chorus programs cannot be adjacent, then the number of different arrangements is ().

A, B, C, D,

6, 5 people in a row, of which at least one of Party A and Party B is at both ends. The number of rows is ()

A, B, C, D,

7. Use the numbers 1, 2, 3, 4 and 5 to form five digits, which are not complex, and the even number less than 50000 is ().

A, B, C, D, 60 years old

8. A class committee will be divided into five people, who are the vice monitor, study committee member, labor committee member and sports committee member.

Among them, A can't be a monitor, B can't be a study committee member, and the number of different division schemes is ().

A, B,

C, D,

Answer:

1-8 BBADCCBA

Fill in the blanks

1 、( 1 )( 4p 84+2p 85)÷(P86-P95)×0！ =___________

(2) if P2n3= 10Pn3, then N = _ _ _ _ _ _ _ _ _

2. From the arrangement of four different elements A, B, C and D, the arrangement of three different elements is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

3, 4 boys, 4 girls in a row, girls don't row at both ends, there are _ _ _ _ different arrangements.

4. There are three ten-cent RMB, 1 ten-cent RMB and four 1 RMB. These RMB can be used to form _ _ _ _ _ _ different currencies.

Second, answer the question.

5. Use the six numbers of 0, 1, 2, 3, 4 and 5 to form a five-digit number, and there are no duplicate numbers.

(1) What are the following situations?

① odd number

② divisible by 5.

③ divisible by 15.

④ less than 35 142

⑤ Less than 50000 and not a multiple of 5.

6. If these five digits are arranged from small to large, what is the number 100?

1 × × × ×

1 0 × × ×

1 2 × × ×

1 3 × × ×

1 4 × × ×

1 5 0 2 ×

1 5 0 3 2

1 5 0 3 4

7. How many different ways are there for 7 people in a row under the following circumstances?

(1) add the card head

(2) A does not occupy the head, nor does it occupy the tail.

(3) Party A, Party B and Party C must be together.

(4) There are only two people on both sides.

(5) Party A, Party B and Party C are not adjacent.

(6) A is to the left of B (not necessarily adjacent)

(7) Party A, Party B and Party C are in the order from high to low and from left to right.

(8) Party A does not take the lead, and Party B is not in the middle.

8. Choose three numbers from the five numbers 2, 3, 4, 7 and 9 to form a three-digit number, and there are no duplicate numbers.

(1) How many such three digits are there?

(2) What is the sum of the digits of all three numbers?

(3) What is the sum of these three digits?

Answer:

I. 1, (1)5 (2)8

2.ABC、Abd、ACD、BAC、bad、BCD、CAB、CAD、CBD、DAB、DAC、DBC。

3、8640 4、39

5、①3× =288 ② ③

④ ⑤

6、 = 120 〉 100

=24

=24

=24

=24

=2

7、( 1) =720 (2)5 =3600 (3) =720 (4) =960

(5) = 1440 (6) =2520 (7) =840 (8)

8、( 1) (2) (3)300×( 100+ 10+ 1)=33300

Arrangement and combination exercise

1, if, then the value of n is ()

a、6 B、7 C、8 D、9

There are 30 boys and 20 girls in one class. Now we should select five people from them to form a propaganda group, including boys and girls.

The selection method of no less than 2 students is ()

A, B,

C, D,

3. There are 10 points in the space, five of which are on the same plane, and the rest have no * * * plane, so 10 points can be determined.

The number of coplanar planes is ()

a、206 B、205 C、 1 1 1 D、 1 10

Six different books are distributed to Party A, Party B and Party C, with two books each. The number of different kinds of books is ().

A, B, C, D,

5, by five 1, two 2 arranged into a series containing seven items, then the number of different series is ().

a、2 1 B、25 C、32 D、42

6. Let P 1, P2…, P20 be the points corresponding to the 20 complex roots of the equation z20= 1 on the complex plane, and the number of right triangles whose vertices are ().

a、360 B、 180 C、90 D、45

7, if, then the value range of k is ()

a 、[5， 1 1] B 、[4， 1 1] C 、[4， 12] D、4， 15]

8. There are four different red balls and six different white balls in the pocket. Take out four balls at a time and take out a ball of thread.

Points, take out a white ball and mark 1 point, so the total score is not less than 5 points.

A, B, C, D,

Answer:

1、B 2、D 3、C 4、A 5、A 6、B 7、B 8、C

1, calculation: (1) = _ _ _ _

(2) =_______

2. Put seven identical balls into 10 different boxes. If there are no more than 1 balls in each box, there are _ _ _ _ different ways to put them.

3. There are five points on the edge OA of ∠ AOB, and six points on the edge OB, plus the o point *** 12 points, and the triangle with these 12 points as its vertex has _ _ _ _ _ _.

4. Take any four numbers from the number 1, 2, 3, …, 9 to make their sum odd, then * * * has _ _ _ different methods.

5. Known

6.( 1) How many triangular pyramids are there with the vertex of the cube as the vertex?

(2) How many four pyramids are there with the vertex of the cube as the vertex?

(3) How many pyramids are there with the vertex of the cube as the vertex?

7. Set A has 7 elements, set B has 10 elements, set A∩B has 4 elements, and set C satisfies

(1)C has three elements; (2)C A∪B； (3)C∩B≠φ, C∩A≠φ, and find one of such sets C.

Count.

8. From 1, 2, 3, ... 30, take three unequal numbers at a time so that their sum is a multiple of 3.

* * * How many different ways are there?

Answer: 1, 4902,313,1654,60.

5. Solution:

6. Solution: (1)

(2)

(3)58+48= 106

7. Solution: There are elements 7+ 10-4= 13 in A ∪ B.

8. Solution: Divide these 30 numbers into three categories according to the remainder after division by 3:

A={3，6，9，…，30}

B={ 1，4，7，…，28}

C={2，5，8，…，29}

(1)