4 adults and 3 kids are seated in a row. In how many different ways can they be seated if an adult must occupy the first position in the row?

Question

anonymous · Answer

@satellite73 can u help me out, and see if my answerrs are right?

anonymous · Answer

what abt this question? Private automobile license plates contain three letters followed by three numbers. If there are no other constraints, the number of plates that could be manufactured is

anonymous · Answer

is the answer 17576000

anonymous · Answer

@callisto can u help me out?

callisto · Answer

I'm not sure if it is correct...
No. of ways = 4x 6x5x4x3x2x1 = ... 
The first one is 4 as one of the 4 adults must occupy the first position. So, 4 people can be chosen..

callisto · Answer

Sorry, I mean for the first question :|

callisto · Answer

For the second question, can the numbers/letters be used again?

callisto · Answer

(My English fails me :( )

callisto · Answer

If it can, then I think it is like this:
No. of ways = 26^3 x 10^3 =....
26 => 26 English letters
10 => 10 numbers (0, 1, 2, 3, ..., 7, 8, 9)

anonymous · Answer

@lgbasallote can you double check the first question?

lgbasallote · Answer

uhmm sorry..im not good with permutations and combinations :/

anonymous · Answer

@robtobey can you help me

anonymous · Answer

i think it is $4\times 6!$ 
4 choices for the first seat and then $6!$ for the remaining 6

anonymous · Answer

oh what callisto said above

anonymous · Answer

second one is what callisto said as well
both answers are right