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The count of 4-digit personal identification numbers possible if the number cannot contain a zero is given by: Option B: 6561
If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
For the given case, there are 4 digit locks, each of them can be from {1,2,3,4,5,6,7,8,9}
So each one has 9 options to choose from.
Thus, using the rule of product, we get the total possible personal identification numbers as: [tex]9 \times 9 \times 9 \times 9= 6561[/tex]
Thus, the count of 4-digit personal identification numbers possible if the number cannot contain a zero is given by: Option B: 6561
Learn more about rule of product here:
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