1. -14 points Notes Ask Your Teacher A group of three boys (Alex, Bryan, and Chr
ID: 3196454 • Letter: 1
Question
1. -14 points Notes Ask Your Teacher A group of three boys (Alex, Bryan, and Chris) and six girls Megan, Nancy, Olivia, Pauline, Rebecca, and Suzy) are going to sit together in a row of 9 theater seats. (a) In how many ways can they seat themselves? (b) In how many ways can they seat themselves if the boys all sit together and the girls all sit together? 2. 0r8 points | Previaus Answers My Notes Ask Your Teacher Peg has 4 long-sleeve shirts, 6 short-sleeve shirts, and 6 pairs of pants (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)? 144 (b) Peg is going on a trip to visit a friend and plans to take 3 shirts and 2 pairs of pants. How many possibilities are there for the articles of clothing she chooses to packi (c) Peg is going on a trip to the mountains and plans to, again, take 3 shirts and 2 pairs of pants, but since it is supposed to be chilly she decides that the shirts she takes should all be long sleeve. How many possibilities are there for the articles of clothing she chooses to pack? (d) Peg is going on a business trip and plans to, again, take 3 shirts and 2 pairs of pants. This time she decides that of the shirts she takes AT LEAST ONE should be a long sleeve shirt.How many possibilities are there for the articles of clothing she chooses to pack?Explanation / Answer
(a)
There are 9 positions and 9 persons to be sitted upon.
Options at first position = 9
Option at second position = 8 (1 person out of 9 already took a seat at first position)
....
Option at 9th position = 1 (8 person out of 9 already took a seat at first position)
total combinations = 9*8*7...1 = 9! = 362880
(b)
Choices = combinations among boys x combination among girls x group combination
combination among boys = 3!
combination among girls = 6!
combination of groups = 2
so total combinations = 3! * 6! * 2 = 720*6*2 = 8640
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.