How many different 4-digit personal identification numbers are possible if no digit can be used twice? a. 1,000 b. 5,040 c. 9,000 d. 10,000

5040

Step-by-step explanation:

To Find : How many different 4-digit personal identification numbers are possible if no digit can be used twice?

Solution :

Since we are given that no digit can be used twice

SO, when one digit is used so next digit will be chosen from the remaining digit an so on .

the digits can be 0,1,2,3,4,5,6,7,8,9

Since these are 10 in number

out of these 10 we need to choose 4 but no digit can be used twice

⇒

Formula :

thus using this formula

⇒

⇒

⇒

⇒

Thus  different 5040 number of 4-digit personal identification numbers are possible if no digit can be used twice

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: