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4 digit number

Expert replies
by ruplun » Fri Jul 29, 2011 5:10 am
A 4 digit number is chosen at random.What is the probability that all the digits are different?

a. 1/10
b. 1/9
c. 1/4
d. 63/125
e. 73/125
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Source: — Problem Solving |

by tauseef10jan2004 » Fri Jul 29, 2011 6:33 am
(10/10)*(9/10)*(8/10)*(7/10)
=63/125
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by sunnyjohn » Fri Jul 29, 2011 6:59 am
Total number of way to choose 4 digits number:

__ __ __ __

> first digit can be any number from 1 - 9. Please note, you can not include 0 because left most 0 digit will make the 3 digits number. For ex- 0123, 0456, 0444 etc.

> Second digit could be anything from 0-9.
> thirst digit could be anything from 0-9.
> fourth digit could be anything from 0-9.

total number of ways : 9 * 10 * 10 * 10

Total number of numbers with all 4 digits different:

> First digit could be anything from 1-9.
> One digit has been chosen, second digit could be anything from 1-9 ( minus 1 digit) or 0.
> 2 digits have been chosen, third digit could be anything from 0-9 ( minus 2 digits)
> 4th digit could be anything from 0-9 ( minus 3 digits).

Total number of way: 9 * 9 * 8 * 7

Now you can find an answer.
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