Question

Part ID codes consist of 4 different letters and 3 different digits. How many codes are possible if the letters must be kept together? For example, 34ABCD9 and W AXT 614 are good, but T R67Y Z3 is bad.

Answer 1

a lot
first we can compute the number of ways to do this if the letters are the first 4 slots
by the counting principle it would be \(26^4\times 10^3\)

Answer 2

then we count how many ways we can put the letter in the 7 slots
it is just counting
they could be in the first 4 places,
the second 4 places
the third 4 places or
the last 4 places

you have 4 choices of places to put the letters, so multiply the above answer by 4

Answer 3

thanks! that helped a lot! it all makes sense now!