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
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 6C4 is equal to …
A. 60 B. 30 C. 24 D. 15 E. 12
Answer: D, Explanation:
2. The value of 11C7 is equal to …
A. 18 B. 30 C. 330 D. 720 E. 166320
Answer: C, Explanation:
3. The value of 12C3 is equal to …
A. 15 B. 130 C. 220 D. 820 E. 1320
Answer: C, Explanation:
4. If nC2=28 then n=⋯
A. 5 B. 6 C. 7 D. 8 E. 9
Answer: D, Explanation:
5. If nC(n-2)=21 then n=⋯
A. 7 B. 8 C. 9 D. 10 E. 11
Answer: A, Explanation:
6. If nC_4=35 then n2=⋯
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∙nC2 is …
A. 2 B. 4 C. 6 D. 7 E. 8
Answer: C, Explanation: