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License plate numbers in Aopslandia used to consist of 5 distinct digits. Due to an increase in population, Aopslandia started to allow license plates to have any 5-digit string, even if some digits are the same. How many more license plates are available because of this change?

 

Two boys and three girls are going to sit around a table with 5 different chairs. If the two boys want to sit together, in how many possible ways can they be seated?

 Apr 15, 2019
 #1
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First one

 

Number of possible new plates  =  (10)^5  =  100,000

Number of possible old plates = (10 * 9 *8 * 7* 6)  =  30,240 

Just subtract these to get the answer

 

Second one.....considering that all rotations are the same

The two boys can be seated in 2 ways

And the girls can be seated in 3! ways

So   2 * 3! =  2 * 6  = 12 ways

 

cool cool cool

 Apr 15, 2019

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