Odds and Combinations

Two questions that sound the same and are not: how many ways can this happen, and how likely is it. Both answered exactly, with big numbers kept whole.

Choosing from a set

Things to choose from

How many you take

The lottery shape: six numbers drawn from forty-nine.

How many ways

Dice

How many dice

Sides each

Total you want

Every total

Coin flips

Flips

Heads wanted

Chance of heads

Shared birthdays

People in the room

Possible values

Works for hash collisions too: put the number of possible hashes in the second box.