# math

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how many 4 number combinations can there be from 0-99 without repeating a number?

• math -

100 choose 4, or C(100,4) where
C(n,r) is defined as
C(n,r)=n!/[r!(n-r)!]

Think of choosing the first number out of 100 choices. We can choose the next number from the remaining 99 numbers, then 98, then 97.

By the rule of multiplication of a multi-step experiment, we have
100*99*98*97 possible outcomes, which correspond exactly to C(100,4).

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