SOLUTION: How many ways can you put 62 numbers in a row of 5?

Question 1013647: How many ways can you put 62 numbers in a row of 5?
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many ways can you put 62 numbers in a row of 5?
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Ans: 62P5 = 62*61*60*59*58
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if order is important than p(62,5).
if order is not important than c(62,5)

p is the permutation formula of 62 numbers taken 5 at a time where order is important.

p(62,5) = 62! / (62-5)! = 62! / 57!

c is the combination formula of 62 numbers taken 5 at a time where order is not important.

c(62,5) = 62! / (5! * 57!).

p(62,5) becomes 776520240.

c(62,5) becomes 6471002.

order is important means that multiple sets of the same 5 numbers are considered a different set if the order in which the numbers are presented is different.

1,2,3,4,5 is considered a different set from 5,4,3,2,1 is order is important. they would be counted as two separate sets.

order is not important means that multiple sets of the same 5 numbers are considered to be the same set if the order in which the numbers are presented is different.

1,2,3,4,5 is considered the same set as 5,4,3,2,1 if order is not important.
they would be counted as one set.

the p(n,x) formula counts the same elements in a different order as different sets.

the c(n,x) formula counts the same element in a different order as the same set.

that's why above, p(62,5) = n! / (57!) and c(62,5) = n! / (5! * 57!).

the c(62,5) formula is really the p(62,5) formula divided by 5!.

c(62,5) = p(62,5) / 5!.

p(62,5) = c(62,5) * 5!.

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