# ncr, n=120, r=3?

Relevance
• I'm going to write this as:

C(n,r)

You want to calculate C(120,3)

When doing this by hand, just start by writing the numbers as a fraction:

120

-----

3

Then multiply by the next smaller number on top and bottom. Stop when you get to 1 on the bottom:

120 × 119 × 118

----------------------

.. 3 . × . 2 . × . 1

Now cancel every number in the denominator using common factors. In this case, you can cancel 3 and 2 against a 6 in 120.

20 x 119 x 118

-------------------

. 1. ×. 1 . × 1

When you have canceled everything in the denominator down to ones, multiply the remaining numbers in the numerator:

20 × 119 × 118

280,840

P.S. To double-check your answer, you can just type "120 choose 3" into Google. Or you can type "C(120,3)" into WolframAlpha.

• 120! / (3! * (120 - 3)!) =>

120 * 119 * 118 * 117! / (6 * 117!) =>

120 * 119 * 118 / 6 =>

20 * 119 * 118 =>

20 * (120 - 1) * (120 - 2) =>

20 * (14400 - 240 - 120 + 2) =>

20 * (14400 - 360 + 2) =>

20 * (14042) =>

280840

• (120 • 119 • 118) ÷ (3 • 2 • 1)