Suppose a \"combination\" lock has the numbers 0 to 39 on it. In order to open t

Question

Suppose a "combination" lock has the numbers 0 to 39 on it. In order to open the lock, a person must dial the correct three number sequence like 12 left, 24 right, 6 left.

a) Why is the name "combination" misleading?

b) How many different three-number sequences are possible assuming that numbers can be repeated?

c) How many different three-number sequences are possible if numbers may not be repeated?

d) Sometimes with these types of locks once the first two numbers are determined, the lock will go ahead and open. How many differnet sequences are possible if this is the case?

e) How many different three-number sequences are possible if all three numbers are even numbers?

f) How many different three-number sequences are possible if only the middle number has to be even?

Explanation / Answer

a) the name combination is not misleading but we have different ways to open a lock among the 40 numbers.

b) if the numbers are repeated we have total of 403 ways = 64000 three number sequences

c) if numbers are not repeated we have 40 x 39 x 38 = 59280 ways

d)

e) if three number sequences are even then we have 203 = 8000 ways ( if even numbers are repeated )

20 x 19 x 18 = 6840 ways ( if even numbers are repeated ).

f) if only middle number is even then we have 40 x 20 x 40 = 32000 ways.

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