What is the probability that seven-digit phone number has one or more repeated digits ? The...

What is the probability that seven-digit phone number has one or more repeated digits ?

The leading number can not be zero (0).

Solutions

Expert Solution

We have to find the probability that the seven-digit phone number has one or more repeated digits.

We can do this also in this way:

P(one or more repeated digits) ~=~ 1 - P(no digits repeated.)

Let us first find for "P(no digits repeated.)"

Let us get favorable ways of feeding the digits at its place without repetition.

9 ways (from 1 to 9) excluding 0 as leading number

9 ways (from 0 to 9) excluding the number previously feed, now 0 will be considered.

8 ways (from 0 to 9) excluding the numbers previously feed.

7 ways (from 0 to 9) excluding the numbers previously feed.

6 ways (from 0 to 9) excluding the numbers previously feed.

5 ways (from 0 to 9) excluding the numbers previously feed.

4 ways (from 0 to 9) excluding the numbers previously feed.

So, favorable ways =

Now, total possible ways =

9 ways (from 1 to 9) excluding 0 as the leading number

10 ways (from 0 to 9)

thus, total ways =

Thus,

P(one or more repeated digits) ~=~ 1 - P(no digits repeated.)

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orchestra answered 1 year ago

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