Combinations

The different selections possible from a collection of items are called combinations. The different selections possible from the alphabets A, B, C, taken 2 at a time, are AB, BC and CA.

It does not matter whether we select A after B or B after A. The order of selection is not important in combinations.

To find the number of combinations possible from a given group of items n, taken r at a time, the formula, denoted by nCr is nCr = n! / [r! * (n-r)!]

For example, verifying the above example, the different selections possible from the alphabets A, B, C, taken two at a time are 3C2 = 3! / (2! * (3-2)!) = 3 possible selections

Important Combination formulas

• nCn = 1

• nC0 = 1

• nC1 = n

• nCr = nC(n-r)

The number of selections possible with A, B, C, taken all at a time is 3C3 = 1