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?
Rangpur Higher Secondary 2011/8
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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.
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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
Re: Rangpur Higher Secondary 2011/8
My answer is 480, please check it
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....
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
- Location:bangladesh,the earth,milkyway,local group.
Re: Rangpur Higher Secondary 2011/8
There are four ways in which the five flags can be hoisted...
1st 2nd pole
4 1
3 2
2 3
1 4
In every possibilities of the 4,the five flags can be hoisted in 5! ways...
So the answer is 4*5!=480 ...
1st 2nd pole
4 1
3 2
2 3
1 4
In every possibilities of the 4,the five flags can be hoisted in 5! ways...
So the answer is 4*5!=480 ...
Man himself is the master of his fate...