Using database management information, people must first turn the specific characteristics of things into data that can be processed by computer through human brain

A permutation problem
C(11,0)/1+C(11,1)/2+C(11,2)/3+…… +C(11,11)/12=?
Add another:
Consider the following formula:
1=0+1
2+3+4=1+8
5+6+7+8+9=8+27
10+11+12+13+14+15+16=27+64
………………
Write an equation containing N, which conforms to the above rule

1,C(11,i)/(i+1)=11!/(i!*(11-i)!/(i+1)=11!/((i+1)!*(11-i)!)=12!/(i+1)!*(11-i)!)/12=C(12,i+1)/12C(11,0)/1+C(11,1)/2+C(11,2)/3+…… +C(11,11)/12=C(12,1)/12+C(12,2)/12.+C(12,12)/12=1/12(C(12,1)+C(12,1)...C...

A permutation problem
Team a and team B each have seven players to play in the go arena according to the order arranged in advance. The first player of both teams will compete, the loser will be eliminated, and the winner will compete with the second player of the negative side Until one team member is eliminated, the other team wins, forming a competition process. Then what are the number of possible competition processes?
The answer is 14c7 = 3432, but I can't understand how this formula comes from,

Only one team can win. Only the last set of each game is considered. No matter what kind of game process, the party who wins the last set is the winner (otherwise, the game will continue, and this game is no longer the last one)

A permutation problem!
There are four table tennis players a, B, C and D. through the statistics of past results, in a game, the probability of a winning against B, C and D is 0.6, 0.8 and 0.9 respectively, so what is the probability of a winning two games in three games between a and B
The answer is p = (2 out of 3) * 0.6 * 0.6 * 0.4. I don't understand why I have to multiply that (3 * 2)!

Because this is based on a win, that a can win in any two of the three games, so it should be C32, and the probability of a winning the two games is 0.6, while the probability of a losing the other game is 0.4

A permutation problem,
It is proved that 3a2 + 4a2 + 5A2 + + 100a2 = 2 * (101c3) - 2

Notice that Na2 = 2 (NC2)
And the formula NC2 + NC3 = (n + 1) C3
So there are 3a2 + 4a2 + 5A2 + +100A2
=2（3C2+4C2+5C2+ … +100C2）
=2（3C3+3C2+4C2+5C2+ … +100C2-3C3）
=2（101C3-3C3）
=2（101C3-1）
=2*(101C3)-2

Arrange and combine a topic
There are eight staff members assigned to the two departments. Two of them who can speak English can not be assigned to the same department, and the other three who can use computer can not be assigned to the same department. How many kinds of allocation schemes are there

Method 1
A: 1 in 1: 2 * 3 * 3 = 18
Method 2
A: 1 in 2: 2 * 3 * 3 = 18
There are 36 kinds in total
(but it seems that the other three people should also be divided into two departments, only in number but not in person.)

A combined question is as follows
Set a = {1,2,3,4}. The domain of definition and range of value of function f (x) are a, and for I belong to a, f (I) = / = I. let A1, A2, A3, A4 be any permutation of 1,2,3,4
| a1 | a2 | a3 | a4 |
|f(a1)|f(a2)|f(a3)|f(a4)|
If at least one number in the corresponding position of two tables is different, it is said that they are two different tables?
The answer must be right,

4! * 4! - 4! (all 4 positions are the same) - C_ 4^2C_ 1 ^ 1 * 4! (2 same positions) - C_ 4^1*C_ 2 ^ 1 * 4! (same position) = 9 * 4!
(! For factorial)

Find a permutation problem
How many ways can I throw 9 balls numbered 1 to 9 into the river? (for example, there are only 2 balls, 1 first, 2 first, 1 and 2 together)

Reference to the recursive method
(1,1)=1
(2,1)=1 (2,2)=2
(3,1)=1 (3,2)=6 (3,3)=6
(4,1)=1 (4,2)=14 (4,3)=36 (4,4)=24
(5,1)=1 (5,2)=30 (5,3)=150 (5,4)=240 (5,5)=120
(6,1)=1 (6,2)=62 (6,3)=540 (6,4)=1560 (6,5)=1800 (6,6)=720
(7,1)=1 (7,2)=126 (7,3)=1806 (7,4)=8400 (7,5)=16800 (7,6)=15120 (7,7)=5040
(8,1)=1 (8,2)=254 (8,3)=5796 (8,4)=40824 (8,5)=126000 (8,6)=191520 (8,7)=141120 (8,8)=40320
(9,1)=1 (9,2)=510 (9,3)=18150 (9,4)=186480 (9,5)=834120 (9,6)=1905120 (9,7)=2328480 (9,8)=1451520 (9,9)=362880
There are (9,1) + (9,2) + (9,3) + (9,4) + (9,5) + (9,6) + (9,7) + (9,8) + (9,9) = 1 + 510 + 18150 + 186480 + 834120 + 1905120 + 2328480 + 1451520 + 362880 = 7087261 throwing methods

A problem of arrangement and combination
There are 12 identical balls, numbered 01 ~ 12 in turn, and 8 identical holes, numbered 01 ~ 08 in turn. Now eight balls are randomly selected from 12 balls and put into 8 holes in turn. Q: what's the probability that one of the balls numbered 01 ~ 07 happens to be in the hole with the same number, and that No. 08 is not the ball in hole 08? What's the probability that there are exactly two balls in hole 08? What's the probability of three balls?

Basic event n = C (8,12) M1 (exactly one and oneself in the hole) = C (1,7) * [C (7,11) - C (6,10)] M2 (exactly two) = C (2,7) * [C (6,10) - C (5,9)] m3 (exactly three) = C (3,7) * [C (5,9)] - C (4,8)] P1 = M1 / N1, P2 = m2 / N2, P3 = m3 / N3 note: C (m, n) = n! / [(m-n)! * m!] personal folly

On the problem of permutation and combination Come on!
How many different currency values can be made up of one yuan five jiao three five Fen five Fen four
I have a father's No one can be right Give it to the first

1 to 9 points can be taken. 9 kinds
From dime to dime, 9 kinds
There are 9 kinds from dime 1 to dime 9
There are nine kinds from triangle one to triangle nine
There are 9 kinds from 4.1 to 4.9
There are nine kinds from fifty-one to fifty-nine
There are 54 species;
Five yuan plus, 54 kinds
There are 108 of them

Using database management information, people must first turn the specific characteristics of things into data that can be processed by computer through human brain