Arranjos com Repetição - Calculadora

Q: How do you Calcular nHr?

nHr can be rewritten as a binomial coefficient: nHr = C(n+r-1, r) = C(n+r-1, n-1) .

Q: How does this calculator treat 0^0?

This tool defines n^0 = 1 and treats 0^0 as 1, since the empty sequence is counted as one outcome.

Como usar (3 passos)

Select a mode: n^r for ordered sequences, or nHr for unordered selections (both allow repeats).
Enter n (types) and r (length / picks). Default values show a common PIN example.
Mude para Aproximado quando o modo Exato ficar grande demais para exibir. Copie a URL para compartilhar exatamente o que está vendo.

Resultado

Value: —

Digits: —

Scientific notation: —

Digits and scientific notation help you understand scale even when the exact integer is too large to display.

History

Growth chart (n fixed, r increases)

Shows how fast counts grow as r increases with n fixed. Blue: n^r. Green: nHr (multichoose).

Max r

Permutation (n^r) Combination (nHr)

Step log

Teacher notes

Permutation with repetition (n^r) counts ordered length‑r sequences. Repeats are allowed, so r can exceed n.
Combination with repetition (nHr) counts unordered selections with repeats, and can be rewritten as C(n+r-1, r) (stars and bars).
Boundary checks: both modes return 1 when r = 0. This tool treats 0^0 as 1.
If Exact is rejected, switch to Approx to still get accurate digit counts and scientific notation.
Common confusion: don’t apply r ≤ n to repetition problems; that restriction is for “without repetition”.

Perguntas frequentes

O que é the difference between permutations and combinations with repetition?

Permutations with repetition count ordered sequences (AB ≠ BA). Combinations with repetition count unordered selections (AB = BA), allowing repeats.

How do you Calcular nHr?

nHr can be rewritten as a binomial coefficient: nHr = C(n+r-1, r) = C(n+r-1, n-1).

Can r be larger than n?

Yes. With repetition allowed, you can pick the same type multiple times, so r > n is valid.

Quando devo I use Exact vs Approx?

Use Exact for manageable sizes when you need the full integer. Use Approx when the integer is huge; you still see the digit count and scientific notation.

How does this calculator treat 0^0?

This tool defines n^0 = 1 and treats 0^0 as 1, since the empty sequence is counted as one outcome.