Solve the following variable combination:
c(n,3)=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
