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How many 4-digit personal identification numbers are possible if the number cannot contain a zero? a. 5,040 b. 6,561 c. 9,000 d. 10,000.

Sagot :

The count of 4-digit personal identification numbers possible if the number cannot contain a zero is given by: Option B: 6561

What is the rule of product in combinatorics?

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:

https://brainly.com/question/2763785

Answer:

B

Step-by-step explanation: