Question

a) A group of 50 people are going to run a race. The top three runners earn gold, silver, and bronze medals. b) Creating a nine player batting order from the 14 players on the baseball team. c) There are 30 applicants for four Software Tester positions.

Answer 1

a) n (No. of peoples) = 50

r (No. of prizes) = 3

p(n,r) = p (50,3)

$\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(50,3)=\frac{50!}{(50-3)!} \\ =117600 \end{gathered}$

b) n(No. of players)=14

r (No. of players for Batting)=9

$\begin{gathered} P(14,9)=\frac{14!}{(14-9)!} \\ =726485760 \end{gathered}$

c)n(Total applicants)=30

r(tester positions)=4

$\begin{gathered} P(30,4)=\frac{30!}{(30-4)!} \\ \text{ =}\frac{30!}{26!} \\ \text{ =657720} \end{gathered}$