Answer: C. 358,800,800
Step-by-step explanation:
Total digitrs ( from 0 to 9 ) = 10
Total letter ( from a to z ) = 26
To make the code , we require 4 letters followed by 3 digits .
If letter can be used once ( i.e. repetition is not allowed) , then the number of ways to arrange this sequence of letters = [tex]^{26}P_4[/tex] [By using Permutation]
[tex]=\dfrac{26!}{(26-4)!}=\dfrac{26\times25\times24\times23\times22!}{22!}[/tex]
[tex]=26\times25\times24\times23=358800[/tex]
But repetition is allowed for digits , so number of ways to arrnge 3 digits = [tex]10\times10\times10=1000[/tex]
Now , the total number of ways tio make the code = 358800 x 1000
=358,800
,000
Hence, the correct option is C. 358,800,800.
