Unizor - Combinatorics - Simple Permutations Problems 2
Channel: Zor Shekhtman on UNIZOR Education
Date: 2014-05-21

Problem 1
How many different sequences of letters can be constructed from all the letters of the name of a game "tic-tac-toe" (dashes are not included, all 9 letters participate in every such sequence)?
Answer: 9! / (3!·2!)

Problem 2
We have to schedule 6 lessons for a day at school: Mathematics, Physics, Chemistry, English, History and Geography. The subjects History and Geography are taught by the same teacher and he asked to put these subjects in a schedule following each other in any sequence.
How many different schedules can be made that satisfy this request?
Answer: 10·4! = 240

Problem 3
Simplify and calculate the value of the expression
(10! − 9!) / 8!
Answer: 81

Problem 4
In his will the king left his three kingdoms, Upland, Midland and Downland to his three daughters Mary, Ann and Lisa, specifying only one requirement that Ann should not be in charge of Upland.
How many different ways of satisfying this king's will exist, provided that each daughter should be in charge of only one kingdom?
Answer: 4

Problem 5
You have collected 12 science fiction books: 3 by Isaac Asimov, 4 by Ray Bradbury and 5 by Arthur Clarke. In how many ways you can put them on a shelf so that the books of the same author are next to each other?
Answer: 3! · 3! · 4! · 5!

Problem 6
How many 4-digit numbers exist that are divisible by 5?
Answer: 1800