WORD PROBLEMS ON FACTORIALS WORKSHEET

Problem 1 :

In how many ways is it possible for 15 students to arrange themselves among 15 seats in the front row of an auditorium?

Solution

Problem 2 :

There are 8 greyhounds in a race. How many different orders of finish (first place through eighth place) are possible?

Solution

Problem 3 :

There are ten candidates for a job. The search committee will choose four of them, and rank the chosen four from strongest to weakest. How many different outcomes are possible?

Solution

Problem 4 :

There are 8 horses in a race. If all we are concerned with are the first, second and third place finishers (the trifecta), how many different orders of finish are possible?

Solution

Problem 5 :

Suppose we are going to use the symbols {a, b, c, d, e, f, g, h} to form a 5-character "password" having no repeated characters. How many different passwords are possible?

Solution

Problem 6 : 

There are six greyhounds in a race:

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

We are concerned about who finishes first, second and third. How many different 1^st, 2^nd, 3^rd orders of finish are possible?

A) 120    B)  216      C) 18       D) 15

Solution

Problem 7 :

Homer, Gomer, Plato, Euclid, Socrates, Aristotle, Homerina and Gomerina form the board of directors of the Lawyer and Poodle Admirers Club. They will choose from amongst themselves a Chairperson, Secretary, and Treasurer.

No person will hold more than one position. How many different outcomes are possible?

A) 336    B) 24     C) 512     D) 21

Solution

Problem 8 :

A flutter on the horses There are 7 horses in a race

a)  In how many different orders can the horses finish? 

b) How many trifectas (1^st, 2^nd and 3^rd) are possible?

Solution

Problem 9 :

In how many ways can 5 boys and 4 girls be arranged on a bench if

a) there are no restrictions?

b) boys and girls alternate?

Solution

Problem 10 :

How many arrangements of the letters of the word REMAND are possible if:

a) there are no restrictions?

b) they begin with RE?

c) they do not begin with RE?

Solution

Problem 11 :

How many arrangements are there of the letters of the word SCROOGE?

In how many of these are the O' s together?

Solution

Problem 12 :

How many arrangements are there of the letters from ABACUS in which the A' s are together?

Solution