Question

There are seven stations between Chennai and howrah.How many type of second class tickets
should be printed so as to serve all type of passengers?

Answer 1

I'd say 72. SQL cross join does this:

;with station_list as
(
select 'Chennai' as station union all
--select 'Kharagpur' union all
--select 'Balasore' union all
--select 'Cuttack' union all
select 'Bhubaneswar' union all
select 'Berhampur' union all
select 'Visakhapatnam' union all
select 'Rajahmundry' union all
select 'Vijayawada' union all
select 'Nellore' union all
select 'Gudur' union all
select 'Howrah'
)
select * from station_list a
cross join
station_list b
where
a.station <> b.station

With 9 overall stations and (commented out Kharagpur, Balasore and Cuttack to match your condition with 7 station between Chennai and Howrah) below is the list with destinations in both directions. Remove comment to have a complete list if necessary. The math is the n choose k * 2 (2 is to serve both destinations south - north and north south). If you don't do SQL consider wolfram with Binomial[9, 2] giving you 36 (one direction). The function subsets would give you an encoded list (also one direction). Otherwise the results below. Does it make sense?

Chennai Bhubaneswar
Chennai Berhampur
Chennai Visakhapatnam
Chennai Rajahmundry
Chennai Vijayawada
Chennai Nellore
Chennai Gudur
Chennai Howrah
Bhubaneswar Chennai
Bhubaneswar Berhampur
Bhubaneswar Visakhapatnam
Bhubaneswar Rajahmundry
Bhubaneswar Vijayawada
Bhubaneswar Nellore
Bhubaneswar Gudur
Bhubaneswar Howrah
Berhampur Chennai
Berhampur Bhubaneswar
Berhampur Visakhapatnam
Berhampur Rajahmundry
Berhampur Vijayawada
Berhampur Nellore
Berhampur Gudur
Berhampur Howrah
Visakhapatnam Chennai
Visakhapatnam Bhubaneswar
Visakhapatnam Berhampur
Visakhapatnam Rajahmundry
Visakhapatnam Vijayawada
Visakhapatnam Nellore
Visakhapatnam Gudur
Visakhapatnam Howrah
Rajahmundry Chennai
Rajahmundry Bhubaneswar
Rajahmundry Berhampur
Rajahmundry Visakhapatnam
Rajahmundry Vijayawada
Rajahmundry Nellore
Rajahmundry Gudur
Rajahmundry Howrah
Vijayawada Chennai
Vijayawada Bhubaneswar
Vijayawada Berhampur
Vijayawada Visakhapatnam
Vijayawada Rajahmundry
Vijayawada Nellore
Vijayawada Gudur
Vijayawada Howrah
Nellore Chennai
Nellore Bhubaneswar
Nellore Berhampur
Nellore Visakhapatnam
Nellore Rajahmundry
Nellore Vijayawada
Nellore Gudur
Nellore Howrah
Gudur Chennai
Gudur Bhubaneswar
Gudur Berhampur
Gudur Visakhapatnam
Gudur Rajahmundry
Gudur Vijayawada
Gudur Nellore
Gudur Howrah
Howrah Chennai
Howrah Bhubaneswar
Howrah Berhampur
Howrah Visakhapatnam
Howrah Rajahmundry
Howrah Vijayawada
Howrah Nellore
Howrah Gudur