Enter combination with variable

Solve the following variable combination:

nc3=165

Calculate r - 1

r = 3, So 3 - 1 = 2

Expand our factorial to 2

n(n - 1)(n - 2)
3!
=
  
165
1

Simplify 3!

3! = 3 x 2 x 1

3! = 6

Simplify

n(n - 1)(n - 2)
6
=
  
165
1

Cross Multiply

n(n - 1)(n - 2) * 1 = 6 * 165

n(n - 1)(n - 2) = 990

Get factor pairs for 990

1 x 990

2 x 495

3 x 330

5 x 198

6 x 165

9 x 110

10 x 99

11 x 90

15 x 66

18 x 55

22 x 45

30 x 33

Arrange in order:

1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990

Find 3 consecutive numbers

Search our factor list for

n(n - 1)(n - 2) = 990

Final Answer


9, 10, 11