Question

There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?

Short answer

There are 720 different orders can the names of the candidates be printed on a ballot.

Step-by-step solution

Given data

There are six candidates.

Concept of Factorial

Factorial is the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.

Thus, factorial seven is written as$\mathbf{1}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathbf{3}\mathbf{\times }\mathbf{4}\mathbf{\times }\mathbf{5}\mathbf{\times }\mathbf{6}\mathbf{\times }\mathbf{7}$.

Calculation of the order of names of the candidates

The six different candidates for governor of state for different orders can the names of the candidates be printed on a ballot is 6! = 720.

Thus, there are 720 different orders can the names of the candidates be printed on a ballot.