# What is 12 CHOOSE 3 or Value of 12C3?

12 CHOOSE 3 = 220 possible combinations.

220 is the total number of all possible combinations for choosing 3 elements at a time from 12 distinct elements without considering the order of elements in statistics & *probability *surveys or experiments. The number of combinations for sample space 12 CHOOSE 3 can also be written as 12C_{3} in the format of **nCr** or **nCk**.

n CHOOSE k | nCk | Combinations |
---|---|---|

11 CHOOSE 2 | 11C2 | 55 |

11 CHOOSE 3 | 11C3 | 165 |

11 CHOOSE 4 | 11C4 | 330 |

12 CHOOSE 2 | 12C2 | 66 |

12 CHOOSE 3 | 12C3 | 220 |

12 CHOOSE 3 | 12C3 | 220 |

## How to Find 12C_{3} or 12 CHOOSE 3?

The below is the complete work with step by step calculation for 12 CHOOSE 3 may helpful for grade school students to learn how find all possible combinations of 12C_{3} for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 12 CHOOSE 3 calculator.

** Workout** :

step 1 Address the formula, input parameters & values

n = 12

k = 3

Find what is 12 CHOOSE 3?

step 2 Substitute n and r values in below nCk formula

nCk = n!/k! (n - k)!

12 CHOOSE 3 =12!/3! (12 - 3)!

step 3 Find the factorial for 12!, 3! & 9!, substitute the corresponding values in the below expression and simplify.

12C3 = 12!/3! (9)!

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12/(1 x 2 x 3) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)

= 10 x 11 x 12/6

= 1320/6

12C3 = 220

220 total possible combinations for 12 CHOOSE 3