Question

An online store randomly assigns shoppers a confirmation code after making a purchase. the confirmation code consists of 4 letters followed by 3 digits. within the confirmation code, letters can be used only once but digits can be repeated. how many different confirmation codes are possible?

A. 14,950,000
B. 5,311,735
C. 358,800,800
D. 358,800

Answer 1

Answer: C. 358,800,800

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 =
`^(26)P_4` [By using Permutation]

`=(26!)/((26-4)!)=(26*25*24*23*22!)/(22!)`

`=26*25*24*23=358800`

But repetition is allowed for digits , so number of ways to arrnge 3 digits =
`10*10*10=1000`

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.