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49 Choose 6 = 13,983,816

There are 13,983,816 ways to choose 6 items from 49 when order does not matter. It is why one ticket in a 6-from-49 lottery has roughly a 1 in 14 million chance of matching all six numbers.

Combinations (49C6)
13,983,816
Permutations (49P6)
10,068,347,520

How 49 choose 6 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 49 and r = 6 gives:

C(49, 6) = 49! / (6! × 43!)
         = 10,068,347,520 / 720
         = 13,983,816

The 43! in the denominator cancels all but the top 6 factors of 49!, so 49 choose 6 is the product of 6 descending terms starting at 49, divided by 6!. That product, 10,068,347,520, is the number of ordered arrangements (49P6); dividing by 6! = 720 removes the duplicate orderings and leaves 13,983,816.

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