suppose a code of five characters,two letters followed by three digits. find

Question

(a) codes
(b) codes with distinct letter
(c) codes with the same letters

Answer 1

Looking at b), I will assume that in a) letters and digits may be repeated.

a) number of codes = 27*27*10*10*10 =

b) Distinct letters, but repeated digits : 27*26*10*10*10 =
distinct letter and distinct codes: 27*26*10*9*8 =

c) codes with same letters but distinct digits: 27*1*10*9*8 =
codes with the same letters and repeated digits : 27*1*10*10*10 =
codes with same letters and same digits: 27*1*10*1*1 = 27*10 =

Answer 2

My mistake!!!!
There are 26 letters, not 27,
So make the necessary changes.

Answer 3

Looking at b), I will assume that in a) letters and digits may be repeated.

a) number of codes = 26*26*10*10*10 = 676000

b) Distinct letters, but repeated digits : 26*25*10*10*10 =650000
distinct letter and distinct codes: 26*25*10*9*8 = 468000

c) codes with same letters but distinct digits: 26*1*10*9*8 =18720
codes with the same letters and repeated digits : 26*1*10*10*10 = 26000
codes with same letters and same digits: 26*1*10*1*1 = 26*10 =260

Answer 4

A club has 25 members.(a) How many ways are there to choose four members of the club to
serve on an executive committee? (b) How many ways are there to choose a president, vice-
president, secretary, and treasurer of the club, where no person can hold more than one
office?