# Combination – Formula n Examples QnA

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

ab=ba; abc=acb=bac=bca=cab=cba.

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

nCk or C(n,k) or C(n,k) or Cnk

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
abc
abd
acd
bcd
abc, acb, bac, bca, cab. cba
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 6C4 is equal to …
A. 60 B. 30 C. 24 D. 15 E. 12 2. The value of 11C7 is equal to …
A. 18 B. 30 C. 330 D. 720 E. 166320 3. The value of 12C3 is equal to …
A. 15 B. 130 C. 220 D. 820 E. 1320 4. If nC2=28 then n=⋯
A. 5 B. 6 C. 7 D. 8 E. 9 5. If nC(n-2)=21 then n=⋯
A. 7 B. 8 C. 9 D. 10 E. 11 6. If nC_4=35 then n2=⋯
A. 25 B. 36 C. 49 D. 64 E. 81   