SOLVING WORD PROBLEMS INVOLVING PERMUTATION

Problem 1 :

There are six greyhounds in a race :

Spot, Fido, Bowser, Mack, Tuffy, William.

How many different 1^st, 2^nd, 3^rd place orders of finish are possible?

Solution

Problem 2 :

If a chess association has 16 teams, in how many different ways could the top 8 positions be filled on the competition ladder ?

Solution

Problem 3 :

Suppose you have the alphabet blocks A, B, C, D and E and they are placed in a row.

a) How many ways could you have ?

b) How many ways we have to end in C.

c)  How many ways to have a form of

___ A ___ B ___

d) How many begin and end with a vowel, A or E ?

Solution

Problem 4 :

In how many ways can 5 different books be arranged on a shelf ?

Solution

Problem 5 :

How many 3 digit numbers can be constructed from the digits 1, 2, 3, 4, 5, 6, 7 each digit may be used :

a) As often as desired

b)  Only once

c)  Only once and the number is odd. 

Solution

Problem 6 :

3 digit number are constructed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 using each digit at most once. How many such numbers :

a) Can be constructed 

b)  end with 5

c) end with 0.

d) are divisible by 5.

Solution

Problem 7 :

In how many ways can 5 different books be arranged on a shelf if 

a) there is no restrictions

b)  books X and Y must be together

c)  Books X and Y never together.

Solution