Permutation & Combination

Every school day morning, Anna goes to Grace's house for breakfast, traveling one of 3 possible routes. Then she goes to Ben's house to help him with his Math homework (ugh), traveling any one of 4 different routes. Then she continues to school, walking any one of 4 possible routes. How many different Routes are there for Anna as she travels from her home to school? __________________

Solution

The possible number of routes through which Anna goes to Grace's house = 3

The possible number of routes through which Anna goes to Ben's house = 4

The possible number of routes through which Anna goes to School = 4

Therefore, the possible number of routes Anna can follow to go School are = * * = 3 * 4 * 4

= 48 Possible Routes

Laura can order 5 different salads and she can top them with any one of 5 different dressings. How many different salad dishes can Laura order? _____________

Solution:

Number of salads = 5

Number of tops = 5

Total number of salad dishes with the combination of tops can be given as = * = 5 * 5

= 25 Salad dishes

Rhode Island license plates are formed by using 3 letters (A - Z) followed by 2 digits (0 - 9). Vermont license plates are formed by using 3 digits (0 - 9) followed by 3 digits (A - Z). If repetition of any letter of digit is allowed, then:

How many RI license plates can be made? _____

How many Vermont license plates can be made? _______

Solution:

The number of ways in which RI license plates can be made = ***

= 26 * 26 * 26 * 10 * 10

= 1,757,600 ways

The number of ways in which Vermont license plates can be made = ***

= 10 * 10 * 10 * 26 * 26 * 26

= 175,760,000 ways

There are 12 students in a certain, special Algebra class, and today is PICTURE DAY!! Only 4 students are allowed to be in the front row. How many different front row arrangements can there be? ________

Solution

The number o different front row arrangements can be given as =

= 495 ways

Students are running for class office. The 5 offices are President, vice-President, Secretary, Treasurer and Provost's aide. In how many ways can these positions be filled? ____

Solution:

The number of ways in which the given positions can be filled can be obtained by using the formula of permutation in the following way:

= 15 * 14 * 13 * 12 * 11 = 360,360 ways

Marla is a bright, young, attractive mathematician who is besieged by suitors. Her social calendar is so full that on any given weekend (Fri-Sat-Sun), she is never without a date. Just last weekend, she was asked to the movies on Friday, the theater on Saturday, and bowling on Sunday. Friday's possible escorts were Al, Bill, Cletus and Dustin. Saturday's were Donny, Elgin and Felix, while Sunday's suitors were Gregoire, Hank, Ichabod, Justin, Kent and Lonnie. In how many unique ways could her ...