Question

Part ID codes consist of 4 dierent letters and 3 dierent digits. How many codes
are possible if the letters must be kept together? For example, 34ABCD9 and
WAXT614 are good, but TR67YZ3 is bad.

Answer 1

i guess none contain the letter "f"

Answer 2

for letters you have 4! positions.
For digits you have 3! positions

Now combining all the possible situations where you can have a IP starting with 0 digits, 1 digit, 2 digits or 3 digits you have 4!

so you have 4! *3! * 4

Answer 3

someone correct me please. Not sure about the final 4

Answer 4

off the top of my head i would count
(letters) # # #
# (letters) # #
# # (letters) #
# # # (letters)

so four different ways, each of which has the same number of possibilities, allowing for repetition
\(10^3\times 26^4\)
my guess is
\[4\times 10^3\times 26^4\]

Answer 5

oops 4 DIFFERENT letters, have to adjust

Answer 6

Oops. Forgot the ammount of digits and letters.


24 A 4 * 10 A 3 * 4

Answer 7

\[4\times 26\times 25\times 24\times 23\times 10\times 9\times 8\]

Answer 8

@satellite73 , thats what i have. In portugal we call that 26*25*24*23 = 26 A 4

Answer 9

ahh i didn't know that notation

Answer 10

satellite, can you explain the reasoning behind the equation?

Answer 11

i think people here in the US use 26P4

Answer 12

was using the 24 letter alphabhete for somehow. Im still stick with my own language :p

Answer 13

\(_{26}P_4\) something like that

Answer 14

i know for Combinations we use C but in portugal we call what i do "Arranjos", thats why we use the A letter

Answer 15

@tim93 i wrote the reasoning above
like having 4 slots 3 each number and 1 for all the letters

Answer 16

Arrangos like Arrangements. i like it better than P for "permutation"

Answer 17

yep that's it! we're are you from ?

Answer 18

Pennsylvania

Answer 19

@tim93 if we put all the letters first we have
\[26\times 25\times 24\times 23\times 10\times 9\times 8\] possibilities because all have to be different
multiply by 4 because letters could go first, second third or fourth

Answer 20

@Diogo i hear Portuguese is very different from most european languages and hard for english speakers to learn. but you have no problems with english. i am jealous

Answer 21

we're forced to learn spanish, french and english on schools. And i spent alot of my life in english forums thats why you can understand what I say :p
English people in the other hand are extremely accommodated with their own language cause its the most spoken in the world and thats why noone teach you the others

Answer 22

we are the losers in this situation