Question

How many arrangements of 3 digits can be formed from the digits 0 through 9?

Answer 1

Answer:  

The required number of arrangements = 900

Step-by-step explanation:

Digits through which the number is to be formed : 0, 1, 2, 3, 4, ......9

Total number of digits available to form the number = 10

Now, No. of digits in the number which is to be formed = 3

So, number of choices available for 1st digit = 9 (0 will not be included)

Number of choices available for 2nd digit = 10

Number of choices available for 3rd digit = 10

So, Total number of arrangements of 3 digits which can be formed from the digits 0 to 9 = 10 × 10 × 9

                    = 900

Therefore, The required number of arrangements = 900

Answer 2

Answer:  The required number of arrangements is 1000.

Step-by-step explanation:   We are given to find the number of arrangements of 3 digits that can be formed from the digits 0 to 9.

Since we are talking about the 3 digit arrangements, not the 3 digit numbers,

so we have 10 options 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the three places in the arrangement.

Therefore, the number of 3 digit arrangements that can be formed is given by

$n=10\times 10\times 10=1000.$

Thus, the required number of arrangements is 1000.