An ID code consists of 4 different letters and 3 different digits. How many codes are possible if the letters must be kept together

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03-08-2016
Mathematics

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An ID code consists of 4 different letters and 3 different digits. How many codes are possible if the letters must be kept together

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caylus caylus · Answer 1 · 2016-08-03T19:45:05+02:00

Hello,

4 different letters and 3 different digits
X represent a letter
- represent a digit
All letters must be kept together:
4 possiblities
XXXX---
-XXXX--
--XXXX-
---XXXX

There are 26 letters.
For each possiblity:
26 choices for the 1 letter
25 choices for the 2 letter
24 choices for the 3 letter
23 choices for the 4 letter

There are 10 digits:
10 choices for the 1 digit
9 choices for the 2 digit
8 choices for the 3 digit

Numbers of codes: 4*26*25*24*23*10*9*8=1033344000.