A license plate consists of three letters followed by three numbers.
a. how many of these license plates are possible
b. how many plates are possible if repetition is not allowed?

Question

A license plate consists of three letters followed by three numbers. 
a. how many of these license plates are possible
b. how many plates are possible if repetition is not allowed?

jim_thompson5910 · Answer

Think of 6 slots: A,B,C,D,E,F
For slots A through C, we have 26 choices because there are 26 letters
For slots D through F, we have 10 choices because there are 10 single digit numbers (0 through 9)

jim_thompson5910 · Answer

So for part (a), we simply multiply out all of the choices for each slot

26*26*26*10*10*10 = ???

pphalke · Answer

17576000

jim_thompson5910 · Answer

good

pphalke · Answer

part b I got 11,232,000

jim_thompson5910 · Answer

`b. how many plates are possible if repetition is not allowed?`

for slot A, we have 26 choices
for slot B, we have 25 choices
for slot C, we have 24 choices


for slot D, we have 10 choices
for slot E, we have 9 choices
for slot F, we have 8 choices


notice how the number of choices decrease each time. This is to reflect we cannot pick the same letter or number twice.

jim_thompson5910 · Answer

26*25*24*10*9*8 = 11,232,000

you are correct