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
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:
combination example i

So, we can get:
combination example ii

Generally can be written
combination formula
combination formula

Example 11:
combination example iii

Exercise Competency Test 11
1. The value of 6C4 is equal to …
A. 60 B. 30 C. 24 D. 15 E. 12
Answer: D, Explanation:
combination example iv

2. The value of 11C7 is equal to …
A. 18 B. 30 C. 330 D. 720 E. 166320
Answer: C, Explanation:

combination example v

3. The value of 12C3 is equal to …
A. 15 B. 130 C. 220 D. 820 E. 1320
Answer: C, Explanation:

combination example vi

4. If nC2=28 then n=⋯
A. 5 B. 6 C. 7 D. 8 E. 9
Answer: D, Explanation:

combination example vii

5. If nC(n-2)=21 then n=⋯
A. 7 B. 8 C. 9 D. 10 E. 11
Answer: A, Explanation:

combination example viii

6. If nC_4=35 then n2=⋯
A. 25 B. 36 C. 49 D. 64 E. 81
Answer: C, Explanation:

combination example

Answer: E, Explanation:
combination qna

8. The value of n which is satisfy the equation 3∙(n+1)C_3=7∙nC2 is …
A. 2 B. 4 C. 6 D. 7 E. 8
Answer: C, Explanation:

combination qna i

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