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69 Choose 5 = 11,238,513

There are 11,238,513 ways to choose 5 items from 69 when order does not matter. It is the number of white-ball combinations in Powerball, where 5 numbers are drawn from 69.

Combinations (69C5)
11,238,513
Permutations (69P5)
1,348,621,560

How 69 choose 5 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 69 and r = 5 gives:

C(69, 5) = 69! / (5! × 64!)
         = 1,348,621,560 / 120
         = 11,238,513

The 64! in the denominator cancels all but the top 5 factors of 69!, so 69 choose 5 is the product of 5 descending terms starting at 69, divided by 5!. That product, 1,348,621,560, is the number of ordered arrangements (69P5); dividing by 5! = 120 removes the duplicate orderings and leaves 11,238,513.

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