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?
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