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A bike lock has a 4 digit combination. Each character can be any digit between 1-9. the only restriction is that all 4 characters cannot be the same (e.g. 1111, 2222, 3333... etc.). How many combinations are possible?


a. 6552 c. 9,990
b. 6561 d. 10,000

Respuesta :

TaeKwonDoIsDead

Answer:

A

Step-by-step explanation:

Let's first assume that the restriction doesn't hold.

So that way we can say that we can put ANY OF THE 9 DIGITS (1-9) on ANY OF THE 4 DIGIT COMBINATIONS.

Hence,

first digit can be any of 1 through 9

second digit can be any of 1 through 9

third digit can be any of 1 through 9

4th digit can be any of 1 through 9

So the total number of possibilities will be 9 * 9 * 9 * 9 = 6561

now, let's take into account the restriction. since all 4 digits cannot be the same, so we need to exclude:

1111

2222

3333

4444

5555

6666

7777

8888

9999

That's 9 numbers. So final count would be 6561 - 9 = 6552

Answer A is right.

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