## Rangpur Higher Secondary 2011/8

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### Rangpur Higher Secondary 2011/8

Problem 8:
At a conference, flags of \$5\$ countries are to be hoisted on \$2\$ poles so that no pole is left empty and all the flags get hoisted. More than one flag must not be placed at the same height of the same pole. Rather, they can be placed above or below an already placed flag. In this manner, more than one flag can be placed serially on a single pole. How many ways can the flags be hoisted?

Mehfuj Zahir
Posts: 78
Joined: Thu Jan 20, 2011 10:46 am

### Re: Rangpur Higher Secondary 2011/8

5 flag can be arranged in two poles having no empty poles in 4 ways.and 5 flages arranged in 5! ways.(how).so the ans is 4.5!=480

Shifat
Posts: 53
Joined: Sun Jul 31, 2011 12:21 pm

### Re: Rangpur Higher Secondary 2011/8

there are four ways, the flags can be flagged like this
1st pole 2nd pole
a. 4 1
b. 3 2
c. 2 3
d. 1 4

case a- the total number of permutations is 4! 5C4= 120(since 4 out of 5 can be selected in 5C4 ways)(all of them in the first pole)
case b- the total number of permutations is 3!2!5C3= 120
case c- the total number of permutations is 2!3!5C2=120
case 4- the total number of permutations is 4!5C1=120

so the total is 480??
I think I got the question right....

Abdul Muntakim Rafi
Posts: 173
Joined: Tue Mar 29, 2011 10:07 pm