Exercise 872Combinatorics › Counting principlesHigh schoolAdded 3 Nov 2026

Arrangements with repetition

#permutations with repetition#multinomial

Statement

How many distinct words can be formed with the letters of "BANANA"?

Hint

Use the multinomial formula: $\frac{6!}{3!\,2!\,1!}$ .

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Counts. B: $1$ , A: $3$ , N: $2$ , total $6$ .

Multinomial. $\frac{6!}{1!\,3!\,2!}=\frac{720}{12}=60$ .

Conclusion. There are $60$ distinct anagrams of "BANANA".