Answer
Number of different ways to elect president, vice president, secretary and treasurer $10_{{P}{_{4}}}$ = 5040
Work Step by Step
Total number of members on its board of directors = 10
Number of members to elect president, vice president, secretary and treasurer = 4
Number of different ways to elect president, vice president, secretary and treasurer $10_{{P}{_{4}}}$ = $\frac{10!}{(10 - 4)! }$ = $\frac{10!}{6! }$ = $\frac{10\times9\times8\times7\times6!}{6! }$ = $10\times9\times8\times7$ = 5040
