So I have a problem that I'm stuck on it since 3 days ago.
You want to participate at the lottery 6/49 with only one winning variant(simple) and you want to know what odds of winning you have:
-at category I (6 numbers)
-at category II (5 numbers)
-at category III (4 numbers)
Write a console app which gets from input the number of total balls, the number of extracted balls, and the category, then print the odds of winning with a precision of 10 decimals if you play with one simple variant.
Inputs:
40
5
II
Result I must print:
0.0002659542
static void Main(string[] args)
{
int numberOfBalls = Convert.ToInt32(Console.ReadLine());
int balls = Convert.ToInt32(Console.ReadLine());
string line = Console.ReadLine();
int theCategory = FindCategory(line);
double theResult = CalculateChance(numberOfBalls, balls, theCategory);
Console.WriteLine(theResult);
}
static int FindCategory (string input)
{
int category = 0;
switch (input)
{
case "I":
category = 1;
break;
case "II":
category = 2;
break;
case "III":
category = 3;
break;
default:
Console.WriteLine("Wrong category.");
break;
}
return category;
}
static int CalculateFactorial(int x)
{
int factorial = 1;
for (int i = 1; i <= x; i++)
factorial *= i;
return factorial;
}
static int CalculateCombinations(int x, int y)
{
int combinations = CalculateFactorial(x) / (CalculateFactorial(y) * CalculateFactorial(x - y));
return combinations;
}
static double CalculateChance(int a, int b, int c)
{
double result = c / CalculateCombinations(a, b);
return result;
}
Now my problems: I'm pretty sure I have to use Combinations. For using combinations I need to use Factorials. But on the combinations formula I'm working with pretty big factorials so my numbers get truncated. And my second problem is that I don't really understand what I have to do with those categories, and I'm pretty sure I'm doing wrong on that method also. I'm new to programming so please bare with me. And I can use for this problem just basic stuff, like conditions, methods, primitives, arrays.
Let's start from combinatorics; first, come to terms:
a
- all possible numbers ( 40
in your test case) t
- all taken numbers ( 5
in your test case) c
- category ( 2
) in your test case So we have
t - c + 1
for numbers which win and c - 1
for numbers which lose. Let's count combinations:
All combinations: take t
from a
possible ones:
A = a! / t! / (a - t)!
Winning numbers' combinations: take t - c + 1
winning number from t
possible ones:
W = t! / (t - c + 1)! / (t - t + c - 1) = t! / (t - c + 1)! / (c - 1)!
Lost numbers' combinations: take c - 1
losing numbers from a - t
possible ones:
L = (a - t)! / (c - 1)! / (a - t - c + 1)!
All combinations with category c
, ie with exactly t - c + 1
winning and c - 1
losing numbers:
C = L * W
Probability:
P = C / A = L * W / A =
t! * t! (a - t)! * (a - t)! / (t - c + 1)! / (c - 1)! / (c - 1)! / (a - t- c + 1)! / a!
Ugh: Not let's implement some code for it:
Code:
// double : note, that int is too small for 40! and the like values
private static double Factorial(int value) {
double result = 1.0;
for (int i = 2; i <= value; ++i)
result *= i;
return result;
}
private static double Chances(int a, int t, int c) =>
Factorial(a - t) * Factorial(t) * Factorial(a - t) * Factorial(t) /
Factorial(t - c + 1) /
Factorial(c - 1) /
Factorial(c - 1) /
Factorial(a - t - c + 1) /
Factorial(a);
Test:
Console.Write(Chances(40, 5, 2));
Outcome:
0.00026595421332263435
Edit:
in terms of Combinations , if C(x, y)
which means "take y
items from x
" we have
A = C(a, t); W = C(t, t - c + 1); L = C(a - t, c - 1)
and
P = W * L / A = C(t, t - c + 1) * C(a - t, c - 1) / C(a, t)
Code for Combinations
is quite easy; the only trick is that we return double
:
// Let'g get rid of noisy "Compute": what else can we do but compute?
// Just "Combinations" without pesky prefix.
static double Combinations(int x, int y) =>
Factorial(x) / Factorial(y) / Factorial(x - y);
private static double Chances(int a, int t, int c) =>
Combinations(t, t - c + 1) *
Combinations(a - t, c - 1) /
Combinations(a, t);
You can fiddle the solution
The technical post webpages of this site follow the CC BY-SA 4.0 protocol. If you need to reprint, please indicate the site URL or the original address.Any question please contact:yoyou2525@163.com.