If there are n balls with different numbers in the bag, is it possible to retrieve any two of the three balls without a serial number? (Downmoon)

Someone asked: Is there one ball in the bag that ranges from 1 to 10? If you want to retrieve three balls, do you have the chance that any two balls in the bag will not be connected? The invitation month took a try today. The algorithm is very general. We are looking forward to communication.

The approximate algorithm is a three-tier loop. One Ball is taken out first, and then any one is taken from the remaining ball, and then ******.

/// <Summary> <br/> /// the bag contains N balls with different numbers. You can retrieve three balls at will, calculate the probability that two balls in three balls are not connected <br/> // by Tony 200909.17 <br/> // <a Title = "" href = "http://blog.csdn.net/downmoon/" mce_href = "http://blog.csdn.net/downmoon/"> welcome to the invitation to exchange, NET technology and software architecture </a> (monthly invitation) 3w@live.cn <br/> // </Summary> <br/> // <Param name = "orgint"> an integer array column </param> <br/> Public static void getprobability (INT [] orgint) <br/>{< br/> int length = orgint. length; <br/> I NT all = 0; // total number of all <br/> int rel = 0; // The total number of adjacent records <br/> foreach (int fi in orgint) <br/> {<br/> // retrieves a ball from the array of length numbers, number: fi <br/> int [] secint = new int [length-1]; <br/> // obtain the array of the remaining nine numbers <br/> int [] temp1 = new int [orgint. length]; <br/> temp1 = (INT []) orgint. clone (); <br/> int T1 = 0; <br/> foreach (INT R1 in temp1) <br/>{< br/> If (Fi! = R1) <br/>{< br/> secint [T1] = R1; <br/> T1 ++; <br/>}< br/> int [] thint = new int [secint. length-1]; <br/> foreach (INT Si in secint) <br/>{< br/> // retrieves a ball from the remaining length-1 number array, number is SI <br/> // obtain the remaining eight number arrays <br/> // console. writeline (FI + "+" + Si + "+"); <br/> int [] temp2 = (INT []) secint. clone (); <br/> int t2 = 0; <br/> foreach (INT R2 in temp2) <br/>{< br/> If (Si! = R2 & R2! = Fi) <br/>{< br/> thint [T2] = R2; <br/> T2 ++; <br/>}< br/> foreach (INT Ti in thint) <br/>{< br/> // you can retrieve a ball from the remaining length-2 number arrays. The number is Ti. <br/> If ((! Isrel (Ti, Si ))&&(! Isrel (FI, Si ))&&(! Isrel (FI, Ti) <br/>{< br/> rel ++; <br/> console. writeline (FI + "+" + Si + "+" + Ti); <br/>}< br/> // This can be obtained by external computation, to save resources <br/> // All ++; <br/>}< br/> All = length * (length-1) * (length-2 ); <br/> console. writeline ("two balls in three balls are not connected:" + REL +! "); <Br/> console. writeline (" all possible three-ball removal: "+ all +! "); <Br/> console. writeline ("the probability that any two of the three balls are not connected:" + (double) REL/All ). tostring (); <br/> console. readkey (); <br/>}< br/> /// <summary> <br/> // compare the adjacent values. <br/> /// </Summary> <br/> /// <Param name = "A"> </param> <br/> // <Param name = "B"> </param> <br/> // /<returns> </returns> <br/> Public static bool isrel (int, int B) <br/>{< br/> If (a + 1) = B) {return true ;}< br/> If (A-1) = B) {return true ;}< br/> return false; <br/>}

Test:

Public static void main (string [] ARGs) <br/>{< br/> int [] orgint = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }; <br/> getprobability (orgint); <br/>}

Test results:

1 + 10 + 7 <br/> 1 + 10 + 8 <br/> 2 + 4 + 6 <br/> 2 + 4 + 7 <br/> 2 + 4 + 8 <br/> 2 + 4 + 9 <br/> 2 + 4 + 10 <br/> 2 + 5 + 7 <br/> 2 + 5 + 8 <br/> 2 + 5 + 9 <br/> 2 + 5 + 10 <br/> 2 + 6 + 4 <br/> 2 + 6 + 8 <br/> 2 + 6 + 9 <br/> 2 + 6 + 10 <br/> 2 + 7 + 4 <br/> 2 + 7 + 5 <br/> 2 + 7 + 9 <br /> 2 + 7 + 10 <br/> 2 + 8 + 4 <br/> 2 + 8 + 5 <br/> 2 + 8 + 6 <br/> 2 + 8 + 10 <br/> 2 + 9 + 4 <br/> 2 + 9 + 5 <br/> 2 + 9 + 6 <br/> 2 + 9 + 7 <br/> 2 + 10 + 4 <br/> 2 + 10 + 5 <br/> 2 + 10 + 6 <br/> 2 + 10 + 7 <br/> 2 + 10 + 8 <br/> 3 + 1 + 5 <br/> 3 + 1 + 6 <br/> 3 + 1 + 7 <br/> 3 + 1 + 8 <br/> 3 + 1 + 9 <br/> 3 + 1 + 10 <br/> 3 + 5 + 1 <br/> 3 + 5 + 7 <br/> 3 + 5 + 8 <br/> 3 + 5 + 9 <br/> 3 + 5 + 10 <br/> 3 + 6 + 1 <br/> 3 + 6 + 8 <br/> 3 + 6 + 9 <br/> 3 + 6 + 10 <br/> 3 + 7 + 1 <br/> 3 + 7 + 5 <br/> 3 + 7 + 9 <br/> 3 + 7 + 10 <br/> 3 + 8 + 1 <br/> 3 + 8 + 5 <br/> 3 + 8 + 6 <br/> 3 + 8 + 10 <br/> 3 + 9 + 1 <br/> 3 + 9 + 5 <br/> 3 + 9 + 6 <br /> 3 + 9 + 7 <br/> 3 + 10 + 1 <br/> 3 + 10 + 5 <br/> 3 + 10 + 6 <br/> 3 + 10 + 7 <br/> 3 + 10 + 8 <br/> 4 + 1 + 6 <br/> 4 + 1 + 7 <br/> 4 + 1 + 8 <br/> 4 + 1 + 9 <br/> 4 + 1 + 10 <br/> 4 + 2 + 6 <br/> 4 + 2 + 7 <br/> 4 + 2 + 8 <br/> 4 + 2 + 9 <br/> 4 + 2 + 10 <br/> 4 + 6 + 1 <br/> 4 + 6 + 2 <br/> 4 + 6 + 8 <br/> 4 + 6 + 9 <br/> 4 + 6 + 10 <br/> 4 + 7 + 1 <br/> 4 + 7 + 2 <br/> 4 + 7 + 9 <br/> 4 + 7 + 10 <br/> 4 + 8 + 1 <br/> 4 + 8 + 2 <br/> 4 + 8 + 6 <br/> 4 + 8 + 10 <br/> 4 + 9 + 1 <br/> 4 + 9 + 2 <br/> 4 + 9 + 6 <br/> 4 + 9 + 7 <br/> 4 + 10 + 1 <br/> 4 + 10 + 2 <br/> 4 + 10 + 6 <br/> 4 + 10 + 7 <br/> 4 + 10 + 8 <br/> 5 + 1 + 3 <br/> 5 + 1 + 7 <br /> 5 + 1 + 8 <br/> 5 + 1 + 9 <br/> 5 + 1 + 10 <br/> 5 + 2 + 7 <br/> 5 + 2 + 8 <br/> 5 + 2 + 9 <br/> 5 + 2 + 10 <br/> 5 + 3 + 1 <br/> 5 + 3 + 7 <br/> 5 + 3 + 8 <br/> 5 + 3 + 9 <br/> 5 + 3 + 10 <br/> 5 + 7 + 1 <br/> 5 + 7 + 2 <br/> 5 + 7 + 3 <br/> 5 + 7 + 9 <br/> 5 + 7 + 10 <br/> 5 + 8 + 1 <br/> 5 + 8 + 2 <br/> 5 + 8 + 3 <br/> 5 + 8 + 10 <br/> 5 + 9 + 1 <br/> 5 + 9 + 2 <br/> 5 + 9 + 3 <br/> 5 + 9 + 7 <br/> 5 + 10 + 1 <br/> 5 + 10 + 2 <br/> 5 + 10 + 3 <br/> 5 + 10 + 7 <br/> 5 + 10 + 8 <br/> 6 + 1 + 3 <br/> 6 + 1 + 4 <br/> 6 + 1 + 8 <br/> 6 + 1 + 9 <br/> 6 + 1 + 10 <br/> 6 + 2 + 4 <br/> 6 + 2 + 8 <br/> 6 + 2 + 9 <br/> 6 + 2 + 10 <br/> 6 + 3 + 1 <br /> 6 + 3 + 8 <br/> 6 + 3 + 9 <br/> 6 + 3 + 10 <br/> 6 + 4 + 1 <br/> 6 + 4 + 2 <br/> 6 + 4 + 8 <br/> 6 + 4 + 9 <br/> 6 + 4 + 10 <br/> 6 + 8 + 1 <br/> 6 + 8 + 2 <br/> 6 + 8 + 3 <br/> 6 + 8 + 4 <br/> 6 + 8 + 10 <br/> 6 + 9 + 1 <br/> 6 + 9 + 2 <br/> 6 + 9 + 3 <br/> 6 + 9 + 4 <br/> 6 + 10 + 1 <br/> 6 + 10 + 2 <br/> 6 + 10 + 3 <br/> 6 + 10 + 4 <br/> 6 + 10 + 8 <br/> 7 + 1 + 3 <br/> 7 + 1 + 4 <br/> 7 + 1 + 5 <br/> 7 + 1 + 9 <br/> 7 + 1 + 10 <br/> 7 + 2 + 4 <br/> 7 + 2 + 5 <br/> 7 + 2 + 9 <br/> 7 + 2 + 10 <br/> 7 + 3 + 1 <br/> 7 + 3 + 5 <br/> 7 + 3 + 9 <br/> 7 + 3 + 10 <br/> 7 + 4 + 1 <br/> 7 + 4 + 2 <br/> 7 + 4 + 9 <br/> 7 + 4 + 10 <br/> 7 + 5 + 1 <br /> 7 + 5 + 2 <br/> 7 + 5 + 3 <br/> 7 + 5 + 9 <br/> 7 + 5 + 10 <br/> 7 + 9 + 1 <br/> 7 + 9 + 2 <br/> 7 + 9 + 3 <br/> 7 + 9 + 4 <br/> 7 + 9 + 5 <br/> 7 + 10 + 1 <br/> 7 + 10 + 2 <br/> 7 + 10 + 3 <br/> 7 + 10 + 4 <br/> 7 + 10 + 5 <br/> 8 + 1 + 3 <br/> 8 + 1 + 4 <br/> 8 + 1 + 5 <br/> 8 + 1 + 6 <br/> 8 + 1 + 10 <br/> 8 + 2 + 4 <br/> 8 + 2 + 5 <br/> 8 + 2 + 6 <br/> 8 + 2 + 10 <br/> 8 + 3 + 1 <br/> 8 + 3 + 5 <br/> 8 + 3 + 6 <br/> 8 + 3 + 10 <br/> 8 + 4 + 1 <br/> 8 + 4 + 2 <br/> 8 + 4 + 6 <br/> 8 + 4 + 10 <br/> 8 + 5 + 1 <br/> 8 + 5 + 2 <br/> 8 + 5 + 3 <br/> 8 + 5 + 10 <br/> 8 + 6 + 1 <br/> 8 + 6 + 2 <br/> 8 + 6 + 3 <br/> 8 + 6 + 4 <br/> 8 + 6 + 10 <br /> 8 + 10 + 1 <br/> 8 + 10 + 2 <br/> 8 + 10 + 3 <br/> 8 + 10 + 4 <br/> 8 + 10 + 5 <br/> 8 + 10 + 6 <br/> 9 + 1 + 3 <br/> 9 + 1 + 4 <br/> 9 + 1 + 5 <br/> 9 + 1 + 6 <br/> 9 + 1 + 7 <br/> 9 + 2 + 4 <br/> 9 + 2 + 5 <br/> 9 + 2 + 6 <br/> 9 + 2 + 7 <br/> 9 + 3 + 1 <br/> 9 + 3 + 5 <br/> 9 + 3 + 6 <br/> 9 + 3 + 7 <br/> 9 + 4 + 1 <br/> 9 + 4 + 2 <br/> 9 + 4 + 6 <br/> 9 + 4 + 7 <br/> 9 + 5 + 1 <br/> 9 + 5 + 2 <br/> 9 + 5 + 3 <br/> 9 + 5 + 7 <br/> 9 + 6 + 1 <br/> 9 + 6 + 2 <br/> 9 + 6 + 3 <br/> 9 + 6 + 4 <br/> 9 + 7 + 1 <br/> 9 + 7 + 2 <br/> 9 + 7 + 3 <br/> 9 + 7 + 4 <br/> 9 + 7 + 5 <br/> 10 + 1 + 3 <br/> 10 + 1 + 4 <br/> 10 + 1 + 5 <br/> 10 + 1 + 6 <br /> 10 + 1 + 7 <br/> 10 + 1 + 8 <br/> 10 + 2 + 4 <br/> 10 + 2 + 5 <br/> 10 + 2 + 6 <br/> 10 + 2 + 7 <br/> 10 + 2 + 8 <br/> 10 + 3 + 1 <br/> 10 + 3 + 5 <br/> 10 + 3 + 6 <br/> 10 + 3 + 7 <br/> 10 + 3 + 8 <br/> 10 + 4 + 1 <br/> 10 + 4 + 2 <br/> 10 + 4 + 6 <br/> 10 + 4 + 7 <br/> 10 + 4 + 8 <br/> 10 + 5 + 1 <br/> 10 + 5 + 2 <br/> 10 + 5 + 3 <br/> 10 + 5 + 7 <br/> 10 + 5 + 8 <br/> 10 + 6 + 1 <br/> 10 + 6 + 2 <br/> 10 + 6 + 3 <br/> 10 + 6 + 4 <br/> 10 + 6 + 8 <br/> 10 + 7 + 1 <br/> 10 + 7 + 2 <br/> 10 + 7 + 3 <br/> 10 + 7 + 4 <br/> 10 + 7 + 5 <br/> 10 + 8 + 1 <br/> 10 + 8 + 2 <br/> 10 + 8 + 3 <br/> 10 + 8 + 4 <br/> 10 + 8 + 5 <br/> 10 + 8 + 6

There are 336 possibilities of No-match between two balls in three balls!

All the three-ball removal possibilities are as follows: 720!

The probability of no connection to any two of the three balls is: 0.466666666666667.

Thank you for your correction.

After reading the replies, it seems that my analysis is not clear enough. At the beginning of this article, the ball 1-10 is a serial number. In my algorithm, numbers are not differentiated,

That is to say, my algorithms are generic and have nothing to do with specific numbers.

Test:

Public static void main (string [] ARGs) <br/>{< br/> int [] orgint = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11 };< br/> getprobability (orgint); <br/>}

 

Change the original number 10 to 11, then the answer is

The possibility of disconnecting two balls in three balls is as follows: 378

Type!

All the three-ball removal possibilities are as follows: 720!

The probability of no connection to any two of the three balls is: 0.525.

Public static void main (string [] ARGs) <br/>{< br/> int [] orgint = {1, 2, 3, 4, 5, 6, 7, 8, 13, 11 };< br/> getprobability (orgint); <br/>}

Change the original number 10 to 11 and the original number 9 to 13, then the answer is changed

The possibility of disconnecting two balls in three balls is as follows: 420

Type!

All the three-ball removal possibilities are as follows: 720!

The probability of no connection to any two of the three balls is: 0.525.

 

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