Combination & Permutation Calculator

Enter n and r to get nCr, nPr, their with-repetition variants, and the full working - all computed exactly with BigInt. Includes a factorial panel and Pascal's triangle row.

Inputs

Total items (n) 0 to 5,000

Chosen items (r) Must satisfy r ≤ n

Combinations nCr

120

n! ÷ (r! × (n − r)!)

Permutations nPr

720

n! ÷ (n − r)!

Combinations with repetition

220

C(n + r − 1, r)

Permutations with repetition

1,000

nʳ

nCr working

nCr = n! ÷ (r! × (n − r)!)
nCr = 10! ÷ (3! × 7!) = 3,628,800 ÷ (6 × 5,040)
nCr = 120

nPr working

nPr = n! ÷ (n − r)!
nPr = 10! ÷ 7! = 3,628,800 ÷ 5,040
nPr = 720

Pascal's triangle

Row n of Pascal's triangle - entry k is C(n, k).

1 10 45 120 210 252 210 120 45 10 1

Row 10 has 11 entries.

Factorial panel

Exact BigInt factorials - try 100 or 1000.

Number (k) 0 to 20,000

479,001,600

12! has 9 digits.