Question

social security number contains nine digits 0 0 0 0 0 0 0 0 0 how many different Social Security numbers can be formed using in a in a numerals from 0-9

Answer 1

First spot: 9 choices (0-9)
Second spot: 9 choices (0-9)
Third spot: 9 choices (0-9)
.
.
.
Ninth spot: 9 choices (0-9)

There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.

9^9 = 387420489 possible social security numbers

Answer 2

1,000,000,000 social Security numbers can be formed using the numerals 0-9.

What is combination?

A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.

The formula for combination is:

$^{n}C_r = \frac{n!}{(n-r)!r!}$

where, n = Total number of items to be selected from.

r = Number of items to be selected.

According to the given problem,

Social security number contains nine digits.

A digit can be any number between 0-9.

For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.

Thus there are $^{10}C_{1}$ ways for filling up first spot.

Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.

Thus there are $^{10}C_{1}$ ways for achieving this.

Same for third, fourth .. . . ninth digit.

Using the formula of combination, total number of ways would be,

= $9 ~times~~ ^{10}C_{1}$

= $(\frac{10!}{1!\times (10-1)!})^9$

= 1000,000,000 ways

Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.

Learn more about combination here:

https://brainly.com/question/13387529

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