Homework 9 part 3 Counting Methods. Answer the following questions using the appropriate counting technique: 1 . How many different seven-digit phone numbers can be formed? 2. How many different five-character passwords can be formed from the lowercase letters of the alphabet if repetition is not allowed? 3. A city council with eight members must elect a four-person executive committee consisting of a mayor, deputy mayor, secretary, and treasurer. How many executive committees are possible? 4. A city council with nine members must appoint a leadership team consisting of mayor, treasurer, and secretary How many teams are possible? 5. The President must assign ambassadors to six different foreign embassies. From a pool of ten candidates, how many different diplomatic teams can she form? 6. Suppose you have 12 music playlists from which you must choose 6 for an upcoming party. If you are not particular about the order in which the music is played, how many 6-playlist sets are possible? 7. How many 6-person lineups can be formed from a 10-player volleyball roster? (Every player plays every position.) 8. How many license plates can be made with seven characters, XXX-YYYY, where X is a letter of the alphabet and Y is a numeral 0-9? 9. How many different three-letter "words" can be formed from the genetic alphabet ACGT