**Combination**

The collection of a group of elements or objects without considering the arrangement or the order is called combination. In combination:

Combination can also be called a grouping or collecting some elements.

The number of combination of *k* elements which are taken from *n* elements which are provided is notated by

_{n}C

_{k}or C(

*n,k*) or C

_{(n,k)}or C

^{n}

_{k}

The combination of 3 letters from the letters: a, b, c, and d are: abc, abd, acd, and bcd. Below is presented the composition between combination of 3 letters and its permutation.

combination | permutation |
---|---|

abd acd bcd |
abd, adb, bad, bda, dab, dba acd, adc, cad, cda, dac, dca bcd, bdc, cbd, cdb, dbc, dcb |

Pay attention that the number of combination = 4 and each combination is consist of three elements, and that tree elements have 3!=6 permutations. And the whole permutation =24.

If we make relation between the number of combination with the number of permutation in the taking of 3 from 4 letters which are provided, then we can get a relation:

So, we can get:

Generally can be written

combination formula

Example 11:

Exercise Competency Test 11

1. The value of

_{6}C

_{4}is equal to …

A. 60 B. 30 C. 24 D. 15 E. 12

Answer: D, Explanation:

2. The value of _{11}C_{7} is equal to …

A. 18 B. 30 C. 330 D. 720 E. 166320

Answer: C, Explanation:

3. The value of _{12}C_{3} is equal to …

A. 15 B. 130 C. 220 D. 820 E. 1320

Answer: C, Explanation:

4. If _{n}C_{2}=28 then *n*=⋯

A. 5 B. 6 C. 7 D. 8 E. 9

Answer: D, Explanation:

5. If _{n}C_{(n-2)}=21 then n=⋯

A. 7 B. 8 C. 9 D. 10 E. 11

Answer: A, Explanation:

6. If _{n}C_4=35 then _{n}^{2}=⋯

A. 25 B. 36 C. 49 D. 64 E. 81

Answer: C, Explanation:

Answer: E, Explanation:

8. The value of _{n} which is satisfy the equation 3∙_{(n+1)}C_3=7∙_{n}C_{2} is …

A. 2 B. 4 C. 6 D. 7 E. 8

Answer: C, Explanation: