How do you calculate the number of combinations without repetition?

For selection without repetition, the number of combinations is calculated using the binomial coefficient formula

\binom{n}{r}=n!/[r!(n-r)!]

. This formula counts the number of ways to choose

r

distinct elements from a set of

n

elements where order does not matter.

Conditions

Identify the total number of elements $n$ and the number of elements to select $r$ .
Calculate the factorial of $n$ , $r$ , and $n-r$ .
Apply the formula $\binom{n}{r}=n!/[r!(n-r)!]$ to find the number of combinations.

For selection without repetition, $\binom{n}{r}=n!/[r!(n-r)!]$ .