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Combinations: a set box, not a padlock

Korean Lotto 6/45 is a set of six balls. If order does not grade the prize, the space is C(45,6)=8,145,060. P(45,6) is much larger. Some games add a bonus ball or order. lottery-odds counts the figure; this essay only splits the names. Do not memorise order like a PIN.

Formulae

C(n,k)=n!/(k!(n−k)!), P(n,k)=n!/(n−k)!. A lotto slip is usually a set.

Bonus

A second-prize bonus ball is another product. Read the official slip.

Split from covering

Net design is another URL.

Responsibility

Vocabulary does not mint a win. Entertainment.

Splitting the names

Combination	C(45,6)=8,145,060
Permutation	P(45,6) ≫
Slip	Usually a set
PIN order	Needless

Arithmetic, not a winning tip.

Lottery odds: honest combinatorics Covering: a net on a table, not an EV engine Digit sum: folding to one place, not a hopper Explore

FAQ

Is a reshuffle another ticket?

6/45 first prize is usually the same set.

Same as lottery-odds?

Counting versus naming — different URLs.

Are permutations harder?

Ordering the same balls grows the space. If the slip ignores order, it is beside the point.

A lock?

No.

For entertainment and arithmetic. Combinatorics, bias, and expected value are not a winning tip or investment advice. Draws are random.