b Permutation locks, because the number of possible codes is actually a permutation.
Practice makes perfect
a We are told that for unlocking a bicycle lock a 4-digit code is needed. Additionally, the code includes digits from 0 to 9 that can be used only once.
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Knowing these restrictions, we will find the probability that all of the digits of the code are even numbers. To do so, let's use the Theoretical Probability Formula.
P(event)=Number of favorable outcomes/Number of possible outcomes
We need to find the number of possible outcomes and the number of favorable outcomes. Note that a different arrangement of the same four digits is a different result. Therefore, we need to find permutations. The number of permutations when taking 4 digits out of 10 is the number of possible outcomes.
Now, we need to find the number of favorable outcomes that are compounds of even numbers.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Note that we have 5 even digits. Therefore, the number of permutations when taking 4 digits out of 5 will be the number of favorable outcomes.
Finally, we can find the probability that all the digits are even by dividing 120 by 5040. Let's do it!
P(All digits are even)&=120/5040
&⇓
P(All digits are even)&=1/42
b We are told that these types of locks are called combinations locks. However, when finding the probability, we used permutations to find the number of possible outcomes and the number of favorable outcomes. Because of this, a mathematician would prefer permutation locks instead.
