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 _{5}P_{3}
= 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 _{5}C_{3}.
The number of ways three things can be arranged in a row is 3!, so

The numbers

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To calculate