Your school is

purchasing a new type of combination lock

for the student lockers. These locks have

40 positions on their dials and use a three-

number combination.

a)How many combinations are possible if

consecutive numbers cannot be the

same?

b)Are there any assumptions that you have

made? Explain.

c)Assuming that the first number must be

dialled clockwise from 0, how many

different combinations are possible?

d)Suppose the first number can also be

dialled counterclockwise from 0. Explain

the effect this change has on the number

of possible combinations.

e)If you need four numbers to open the

lock, how many different combinations

are possible?