# What is 5 CHOOSE 2 or 5C_{2}?

5 CHOOSE 2 = 10 possible combinations.

10 is the total number of all possible combinations for choosing 2 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 2 can also be written as 5C_{2} in the format of **nCr** or **nCk**.

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

4 CHOOSE 1 | 4C1 | 4 |

4 CHOOSE 2 | 4C2 | 6 |

4 CHOOSE 3 | 4C3 | 4 |

5 CHOOSE 1 | 5C1 | 5 |

5 CHOOSE 2 | 5C2 | 10 |

5 CHOOSE 2 | 5C2 | 10 |

## How to Find 5C_{2} or 5 CHOOSE 2?

The below is the complete work with step by step calculation for 5 CHOOSE 2 may helpful for grade school students to learn how find all possible combinations of 5C_{2} for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of this 5 CHOOSE 2 calculator.

** Workout** :

step 1 Address the formula, input parameters & values

n = 5

k = 2

Find what is 5 CHOOSE 2?

step 2 Substitute n and r values in below nCk formula

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

5 CHOOSE 2 =5!/2! (5 - 2)!

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

5C2 = 5!/2! (3)!

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

= 4 x 5/2

= 20/2

5C2 = 10

10 total possible combinations for 5 CHOOSE 2