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To find the number of distinct arrangements of a word with repeated letters, you take the factorial of the total number of letters and divide it by the product of the factorials of the multiplicities of each repeated letter. This corrects for the overcounting caused by treating identical letters as distinct.

Conditions: The word contains repeated letters.; We are finding the number of distinct permutations (arrangements).

To find the number of distinct arrangements of a word with repeated letters, you take the factorial of the total number of letters and divide it by the product of the factorials of the multiplicities of each repeated letter. This corrects for the overcounting caused by treating identical letters as distinct.

Conditions: The word contains repeated letters.; We are finding the number of distinct permutations (arrangements).

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: The selection is made without repetition.; The elements are distinct.; Order does not matter in the selection.

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: The selection is made without repetition.; The elements are distinct.; Order does not matter in the selection.