+0  
 
0
102
3
avatar

Our club has 10 members, and we need to appoint a president, a vice-president, and a secretary. How many ways can we do this if members can hold any number of offices?

 May 28, 2021
 #1
avatar+89 
+1

10P3=720

 May 28, 2021
 #2
avatar+34428 
+1

10 x 10 x 10 = 1000 ways

 May 28, 2021
 #3
avatar
0

If a person could only have at most 1 office at a time, then we would be "choosing" 3 people from the 10. This is why tmatthews answered \(\binom{10}{3}\). However, since a person can have more than one office, then there are 10 options for the President, 10 for the vice President, and 10 for the secretary. This gets us 10 x 10 x 10 = 1000.

 May 28, 2021

32 Online Users