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# How many 3 number combinations are there in the numbers 1 to 6?

Updated: 9/11/2023

Wiki User

12y ago

I'm not confident that my calculations are correct; I'm withdrawing my attempt. My guess is that if repetition of numbers is allowed, and if the order of the numbers is important (663 is distinct from 366) then there are 216 possibilities. With repetition but no particular order, I think the number is 186 possibilities.

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Combinatorial theory is based on the premise that the order of the numbers does not matter. So that 234, 243, 432 are all the same.

If no repetition is permitted, there are 6C3 = 6*5*4/(3*2*1) = 20 combinations.

If repetition is allowed,

there are a further 6*5 = 30 combinations with a pair and a singleton

and another 6 triplets.

All in all 56 combinations.

Although NOT strictly part of the answer, the number of permutations (order DOES matter), without repeat, are

6*5*4 = 120

and finally, if repeats are allowed, the number is 6*6*6 = 216 as in the previous answer.

However, remember that "combination" locks are a misnomer and in mathematics the order does not matter in combinations.

Wiki User

12y ago

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Q: How many 3 number combinations are there in the numbers 1 to 6?
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