Yet Another Cycling Forum
General Category => The Knowledge => OT Knowledge => Topic started by: Basil on 11 March, 2020, 07:55:07 pm
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How do I work out the number of possible combinations of any 3 numbers from 25?
I keep thinking I've got the formula, then my brain fails.
TIA
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https://www.mathwords.com/c/combination_formula.htm
?
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Is it similar to the National Lottery but with different numbers?
http://www.webmath.com/lottery.html
You want to calculate your odds at winning the lottery given:
You must choose a sequence of 3 numbers correctly to win.
The lowest number you can choose is 1
The highest number you can choose is 25
A given number can only be chosen once per try (per lottery ticket, etc.)
When you select your 1st number, you have 25 numbers to choose from, and...
...a 1 in 25 chance of picking the right one.
(Mathematically, 1 in 25 is represented by the numerical fraction 1/25 or 0.040000.)
When you select your 2nd number, you have 24 numbers to choose from, and...
...a 1 in 24 chance of picking the right one.
(Mathematically, 1 in 24 is represented by the numerical fraction 1/24 or 0.041667.)
When you select your 3rd number, you have 23 numbers to choose from, and...
...a 1 in 23 chance of picking the right one.
(Mathematically, 1 in 23 is represented by the numerical fraction 1/23 or 0.043478.)
In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply.
So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.
1/25 × 1/24 × 1/23 = 1/13800
So, at this point, your odds of winning are 1 in 13800. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 3 numbers can be written down, which for 3 numbers is 3! (3 factorial) or 6. Divide 13800 by 6 to account for this, to get 2300.
In other words, there are 6 different ways that the 3 numbers you choose can be filled out on your lottery ticket--if you choose your 3 numbers correctly, any of these ways will make a winning ticket.
That's it! You have a
1 in 2,300
chance of winning the lottery you described.
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Probably you want either a combination or a permutation. If the order is irrelevant, i.e. 1, 2, 3 is the same as 3, 2, 1 and 2, 1, 3, etc. then you have a combination. If order matters, i.e. 1, 2, 3 and 2, 3, 1 are distinct, then you have a permutation.
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I guess it depends on whether you could have the same number 3 times or not.
I got 2.5852017e+24. Which is obviously very far away....
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Suggestion: use a descriptive thread title eg "Maths, calculating combinations".
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Here you go
https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
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Thanks all. Those are very complicated formulas. I have no idea what n! means. What is wrong with a simple
(25÷3)×(24÷2)×(23)
Thanks again.
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Thanks all. Those are very complicated formulas. I have no idea what n! means. What is wrong with a simple
(25÷3)×(24÷2)×(23)
Thanks again.
6! Is shorthand for 6x5x4x3x2x1
It saves a lot of typing when numbers get larger.
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Oh. Thanks. That's very useful to know. :thumbsup:
*wanders off to play with numbers* :D
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Thanks all. Those are very complicated formulas. I have no idea what n! means. What is wrong with a simple
(25÷3)×(24÷2)×(23)
Thanks again.
6! Is shorthand for 6x5x4x3x2x1
It saves a lot of typing when numbers get larger.
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Like that.
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Isn't that factorial?
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Yes, “factorial” is how you pronounce ‘!’
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just guessing:
for the first selection of three numbers:
First you chose from range of 25 (call it 1a),
second from a range of 24 (as you cannot chose the same number twice)
and third from range of 23
So the possibilities for any selection of three numbers from 25 is
25 x 24 x 23
For the next selection, having done all possible combinations for 1a it gets dropped, so
First you get to chose from a range of 24,
Second from range of 23,
and third from a range of 22
combinations are = 24 x 23 x 22
and so on...
add up all combinations
or in shorthand (factorials)
= 25! x 24! 23!
= 2.5852 x (10)22 (and a bit)
Which explains why none of us win the lottery on a regular basis!
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No, basils answer was correct - (25 x 24 x 23)/ (3x2x1)
Which comes to 2300. No need for a calculator.
This assumes you aren’t allowed repeated numbers e.g. 7,7,7 is not allowed.
If you are allowed repeated numbers it is 25x25x25
(You have 25 choices each time)
If the order is important e.g. 7,8,9 is considered different to 7,9,8 then the answer is (25x24x23) = 13800
The reason for the dividing by 6 to get the actual answer of 2300 is that if you take the 13800 you have counted each triplet 6 times - e.g. for 7,8,9
7,8,9
7,9,8
8,9,7
8,7,9
9,7,8
9,8,7
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Got it, thanks!
I make that 0% for me.
(No need for a calculator.)
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Isn't that factorial?
Yep secondary school maths, around age 13 from memory.
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Got it, thanks!
I make that 0% for me.
(No need for a calculator.)
You had the first digit of the answer correct and the last two digits as well. It was only the second digit that was wrong (and you had inserted a few extra). 75%, A
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75%, A
Modern marking!
Had it been invented sooner,
I would be a mathematical genius now!