A course identification code is made up of for upper case le

A course identification code is made up of for (upper- case) letters followed by three decimal digits. the four letters from the department code,while the three digit form the code of the course subject area. The english alphabet has 26 letters.

A) how many different four-letter department codes are there ?

B) How many different three digit subject codes are there ?

C) how many different there-digit subject codes are there that begin with 1?

D) how many different three digit subject codes or there that do not begn with 1?

E) how many different four-letter department codes are there, if no letter can be repeated ?

Solution

a)

total number of different four letter department codes = 26 *26 * 26 * 26 = 456976

since each letter can be any of the 26 alphabets

b)

total number of different three digit subkect codes = 10 * 10 * 10 = 1000

c)

total number of three digit codes that begin with 1 = 1 * 10 * 10 = 100

d)

total number of three digits that does not begin with 1 = 1000 -100 = 900

e)

total number of four letter department codes if no letter can be repeated

= 26 * 25 * 24 * 23

= 358800