##### In how many different ways can these number be arranged in a row of 6, from 0 to 60?

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

From 0 to 60 in a row of 6, I need all possible combination for an example:

36 30 40 5 49 38

6 2 55 36 5 8

42 10 1 43 55 47

Apr 25th, 2015

This is the question of choosing a combination of 6 numbers from 61 numbers (0...60) where the order is important.

The answer is the k-combination formula ((n,k) usually it is vertical)

(n,k) = (n-k)!/k! = 57!/6! = 57!/24 (factorial (!) n is defined as 1*2*3....(n-1)*n)

57! is a huge number. It can be estimated as

57! approx sqrt(2*pi*57)*(57/e)^57 = 4 * 10^76  or 4E76  (approx = equal approximately)

Thus

57!/6! approx 4 * 10^76/24= 1.7 *10^75 or 1.7E75

Apr 25th, 2015

Correction:

I needed to calculate to 55 (61-6)  instead of 57 in the above

Apr 25th, 2015

This is the question of choosing a combination of 6 numbers from 61 numbers (0...60) where the order is important.

The answer is the k-combination formula ((n,k) usually it is vertical)

(n,k) = (n-k)!/k! = 55!/6! = 55!/24 (factorial (!) n is defined as 1*2*3....(n-1)*n)

57! is a huge number. It can be estimated as

57! approx sqrt(2*pi*55)*(57/e)^55 = 1.3 * 10^73  or 1.3E73  (approx = equal approximately)

Thus

55!/6! = 1.3*10^75 /24 = 5.4*10^71 =5.4E71

Apr 25th, 2015

Thank you for taking your valuable time to respond to my inquiry, do you think there's a way to generate a list via a program, I can't do it manually ?

Apr 25th, 2015

Thank you for taking your valuable time to respond to my inquiry, do you think there's a way to generate a list via a program, I can't do it manually ?

Apr 25th, 2015

Of course you can think of an algorithm to program it by using certain order. For example

you first print the combinations with  only the first number change: 0,0,0,0,0,0 1,0,0,0,0,0, 2,0,0,0,0,0....Then on each of the 61 numbers you change the 2nd digit from the left, etc..

But this is an enormous list. I don't think there is enough paper in the world to print it on or that you can view it on a screen in your lifetime.....

Apr 25th, 2015

...
Apr 25th, 2015
...
Apr 25th, 2015
Oct 24th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle