Find the number of possible ways of selecting a manager assi

Find the number of possible ways of selecting a manager, assistant manager, and team leader from a group of 14 members (show your work):

Find the number of possible license plates that can be made using three (3) letters followed by three (3) digits (show your work):

total number of members in the group

selecting a manager, assistant manager and team leader from a group of members.

Here the order is not important, so you can select a manager, assistant manager or team leader in any order.

Number of ways to select three persons from a group 14 members in 14C3 ways = 14!/(3!*11!)= (14*13*12)/6

= 14*13*2 = 364

There are 26 letters, three letters can be selected from 26 letters (with repitions) in 26*26*26 ways

There are 10 digits out of which 3 digits can be selected (with repitions ) in 10*10*10 ways.

the number of possible license plates that can be made using three letters followed by three digits is

=26*26*26*10*10*10=17576*1000=17,576,000