Question 1

a) A computer user must create 6-letter password using 6 different letters of the alphabet. Capitalization does not matter, but of course order does matter. How many different 6-letter passwords with no repeated letters are possible?

b) A medical student is given a list of 13 hospitals and must select 5 of them at which she would be interested in serving as an intern. The order of selection is not important. In how many ways can she make her selection?

c) The County Parks and Recreation Board is planning to upgrade the playground equipment in 3 of the 18 county-owned parks in the first phase of making their parks safer for the children who play there. In how many ways can they select 3 of those parks to receive the upgrades in the first phase?

d) The owner of a bridal boutique must select 4 dresses to display in the store window every week. If each week she has 13 dresses from which to choose, and the order in which they are displayed is not important, in how many ways can she select 4 dresses?

e) As part of a test with young children, a psychologist asks his subject to select 3 favorite toys from a set of 9 brightly colored toys. If the order of selection is not important, how many sets of 3 toys can the child select?