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Combinations
 
The number of ways in which three members can be chosen from among five and arranged in a row    =    The number of ways in which three members can be chosen from among five, and arranged in a row

The only difference between the two sides of this equation is the comma on the right-hand side.

The left-hand side is 5P3 = 5·4·3 = 60.

The right-hand side represents the compound task of first choosing three member from among five, and then arranging them in a row.

The number of ways in which three members can be chosen from among five is denoted by 5C3. The number of ways three things can be arranged in a row is 3!, so

5P3 = 5C3·3!
This allows us to compute
5C3 = 5P3/3! =  5·4·3/3·2·1 = 10

The numbers nC2 are known as triangle numbers.

To play with nC2, click here.

To calculate nCr and nPr, click here.