Question

How many licence plates may be made using either two distinct letters followed by four digits or two digits followed by 4 distinct letters where all digits and letters are distinct?

Answer 1

Answer:

3276000

32292000

Step-by-step explanation:

Case 1

two distinct letters followed by four digits (distinct)

Two distinct letter

1st letter can be chooses from 26 alphabates

2nd letter can be chosen from 25 Alphabates ( as already chosen alphabtes can not be used again)

so 26 * 25 = 650

Four Digits = 10*9*8*7 = 5040  ( 10 digits 0-9 & Distinct)

So total license Plates can be made = 650 * 5040  = 3276000

Case 2

two distinct digits  followed by four distinct  Letters

Two Digits

1st Digit can be chosen from 10 digits (0-9)

2nd digit can be chosen from 9 digits ( as already chosen digit can not be used again)

so 10*9 = 90

Four distinct letter

1st letter can be chooses from 26 alphabates

2nd letter can be chosen from 25 Alphabates ( as already chosen alphabtes can not be used again)

Similarly 3rd letter from 24 & 4th letter from 23 Alphabets can be chosen

so 26 * 25*24*23 = 358800

So total license Plates can be made = 90 * 358800  = 32292000