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Examples of Combination problems

Combination problems Post by natttt
Posted on 2011-03-22 00:04:55
In permutations, the order is all important -- we count abc as different from bca. But in combinations we are concerned only that a, b, and c have been selected. abc and bca are the same combination.

Example 1. How many combinations are there of 5 distinct things taken 4 at a time?
5C4 = 5· 4· 3· 2/1· 2· 3· 4 = 5

Example 2. Evaluate 8C6.
8C6 = 8· 7· 6· 5· 4· 3/1· 2· 3· 4· 5· 6 = 28

Example 3. Evaluate 8C2.
8C2 = 8· 7/1· 2 = 28

Example 4. Write out nC3.
nC 3 = n(n &#8722; 1)(n &#8722; 2)/1· 2· 3

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