how many possible combinations of 6 numbers

If you are asking “how many possible combinations of 6 numbers can be chosen from a larger pool of numbers, where order does not matter and no repeats are allowed,” the standard answer uses the combinations formula (n6)\binom{n}{6}(6n), where nnn is the size of the pool.
Understanding the core idea
When people search for how many possible combinations of 6 numbers , they are usually thinking of lottery-style picks:
- You have a pool of nnn distinct numbers (like 1–49 or 1–50).
- You choose 6 of them.
- The order you pick them in does not matter.
In combinatorics, this is counted with the formula for combinations.
Number of combinations=(n6)=n!6!(n−6)!\text{Number of combinations}=\binom{n}{6}=\frac{n!}{6!(n-6)!}Number of combinations=(6n)=6!(n−6)!n!
Concrete examples
Here are some common cases people care about:
- From 50 numbers (like some lottery games):
(506)=15,890,700\binom{50}{6}=15{,}890{,}700(650)=15,890,700 different 6-number combinations.
- From 49 numbers (classic 6-from-49 lotteries):
The same formula applies: (496)\binom{49}{6}(649) combinations (computed with the same style as the 50-case above).
These counts show why winning lottery-style games is so unlikely: your 6-number ticket is just 1 out of many millions of possible 6-number combinations.
Mini FAQ style view
- If you know the pool size nnn:
Plug it into (n6)\binom{n}{6}(6n) to get how many possible combinations of 6 numbers you can form.
- If order matters instead (like a 6-digit code):
That becomes a permutations problem and uses a different formula, which is much larger than the combinations count, because each ordering of the same 6 numbers is treated as distinct.
Information gathered from public forums or data available on the internet and portrayed here.