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45 Choose 6 = 8,145,060

There are 8,145,060 ways to choose 6 items from 45 when order does not matter. It is the number of possible draws in a 6-from-45 lottery such as Saturday Lotto.

Combinations (45C6)
8,145,060
Permutations (45P6)
5,864,443,200

How 45 choose 6 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 45 and r = 6 gives:

C(45, 6) = 45! / (6! × 39!)
         = 5,864,443,200 / 720
         = 8,145,060

The 39! in the denominator cancels all but the top 6 factors of 45!, so 45 choose 6 is the product of 6 descending terms starting at 45, divided by 6!. That product, 5,864,443,200, is the number of ordered arrangements (45P6); dividing by 6! = 720 removes the duplicate orderings and leaves 8,145,060.

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