# What is 10 CHOOSE 5 or Value of 10C5?

10 CHOOSE 5 = 252 possible combinations.

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

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

9 CHOOSE 4 | 9C4 | 126 |

9 CHOOSE 5 | 9C5 | 126 |

9 CHOOSE 6 | 9C6 | 84 |

10 CHOOSE 4 | 10C4 | 210 |

10 CHOOSE 5 | 10C5 | 252 |

10 CHOOSE 5 | 10C5 | 252 |

## How to Find 10C_{5} or 10 CHOOSE 5?

The below is the complete work with step by step calculation for 10 CHOOSE 5 may helpful for grade school students to learn how find all possible combinations of 10C_{5} for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 10 CHOOSE 5 calculator.

** Workout** :

step 1 Address the formula, input parameters & values

n = 10

k = 5

Find what is 10 CHOOSE 5?

step 2 Substitute n and r values in below nCk formula

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

10 CHOOSE 5 =10!/5! (10 - 5)!

step 3 Find the factorial for 10!, 5! & 5!, substitute the corresponding values in the below expression and simplify.

10C5 = 10!/5! (5)!

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

= 6 x 7 x 8 x 9 x 10/120

= 30240/120

10C5 = 252

252 total possible combinations for 10 CHOOSE 5