2.3 Permutations practice 2

In how many different ways can the letters of the word “OPTICAL” be rearranged so the vowels always come together?

In how many different ways can the letters of the word “CORPORATION” be rearranged so the vowels always come together?

The grid shown represents the street of a city.

Determine how many routes from A (Karen’s house) to B (Anna’s house) are possible if Karen only travels south or east?

Annabelle, Bryce, Caitlin, Dorothy, Ethan, and Francis are to be seated along one side of a rectangular table. How many different seating arrangements are possible if:

(a) There are no restrictions?

(b) The boys cannot sit next to each other?

(c) Annabelle cannot sit next to Caitlin, and the boys must sit together

The grid shown represent the street of downtown Taipei. Determine how many routes from A (Alvin’s house) to B (Rem’s house) are possible if Henri only travels south or east.

(Calculator) The grid shown represent the streets of downtown Taipei. Determine how many routes from A(Williams’ house) to B(Justin’s house) are possible if William only travels south or east.

Annabelle, Claire, Emily, Joseph, Louis, Max, and Ryan are lining up to purchase tickets to the middle school musical The wizard of Oz. How many different arrangements possible when they line up if:

(a) There are no restrictions

(b) The girls have to be together

(c) Joseph has to be next to Emily

How many even four-digit numbers can be made from the digits 0, 2, 3, 4, 5, or 7 if no digit can be repeated?

(Calculator) Five different mathematics books are to be arranged on Ms. Noda’s desk. How many arrangements are possible?

(Calculator) How many different words (real or imaginary) can be formed using all the letters in the word REARRANGE?

(Calculator) In a dog show, there are three Pomeranians, five Golden Retrievers, two Great Pyrenees, and six English Terriers. If the dogs of the same breed are considered identical, in how many ways can the dogs be lined up in front of the judges?

(Calculator) Twelve mice run in a race. How many different ways can they come in first, second, and third places? Assume that there are no ties.