# What is 5 CHOOSE 3 or Value of 5C3?

5 CHOOSE 3 = 10 possible combinations.

10 is the total number of all possible combinations for choosing 3 elements at a time from 5 distinct elements without considering the order of elements in statistics & *probability *surveys or experiments. The number of combinations for sample space 5 CHOOSE 3 can also be written as 5C_{3} in the format of **nCr** or **nCk**.

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

4 CHOOSE 2 | 4C2 | 6 |

4 CHOOSE 3 | 4C3 | 4 |

4 CHOOSE 4 | 4C4 | |

5 CHOOSE 2 | 5C2 | 10 |

5 CHOOSE 3 | 5C3 | 10 |

5 CHOOSE 3 | 5C3 | 10 |

## How to Find 5C_{3} or 5 CHOOSE 3?

The below is the complete work with step by step calculation for 5 CHOOSE 3 may helpful for grade school students to learn how find all possible combinations of 5C_{3} for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 5 CHOOSE 3 calculator.

** Workout** :

step 1 Address the formula, input parameters & values

n = 5

k = 3

Find what is 5 CHOOSE 3?

step 2 Substitute n and r values in below nCk formula

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

5 CHOOSE 3 =5!/3! (5 - 3)!

step 3 Find the factorial for 5!, 3! & 2!, substitute the corresponding values in the below expression and simplify.

5C3 = 5!/3! (2)!

=1 x 2 x 3 x 4 x 5/(1 x 2 x 3) (1 x 2)

= 4 x 5/2

= 20/2

5C3 = 10

10 total possible combinations for 5 CHOOSE 3