Seven men arrive at a meeting, and each of them shakes hands once with each of the others. How many handshakes does that make?Iam trying to solve it two hours ? hhhhh ^_*Show me your cleverness
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Thanx alot for all these information . I hate maths coz of my ego teacher in secondary school
Anyway .. Thats realy nice friend
Have anice day
Zahra said:
hi
a part of Algebra in mathematics is related to solving of these kinds of problems which is called Combination:An arrangement of r objects,WITHOUT regard to ORDER and without repetition,selected from n distinct objects is called a combination of n objects taken r at a time.
The number of such combinations is denoted by:c(n,r)=n!/(r!*(n-r)!) in which n! is equal to n*(n-1)*(n-2).......*2*1 Example : In a conference of 9 schools, how many intraconference football games are played during the season if the teams all play each other exactly once?
When the teams play each other, order does not matter, we are counting match ups. For each game there is a group of two teams playing. So we can use combinations to help us out here. First we need to find n and r : If n is the number of teams we have to choose from, what do you think n is in this problem? If you said n = 9 you are correct!!! There are 9 teams in the conference. If r is the number of teams we are using at a time, what do you think r is? If you said r = 2, pat yourself on the back!! 2 teams play per game. Let's put those values into the combination formula and see what we get: c(9,2)=9*8/2=36
so in the problem you shared we can say that for shaking hands we need 2 persons and these 2 persons are chosen among the 7 persons at that meeting.here it doesn't differ that the person number 1 shakes hands with the number 2 or number 2 shakes hands with number 1.so order is not important here.so we can use Combination here.the answer will be: c(7,2)=7!/5!*2!=7*6/2=21
a part of Algebra in mathematics is related to solving of these kinds of problems which is called Combination:An arrangement of r objects,WITHOUT regard to ORDER and without repetition,selected from n distinct objects is called a combination of n objects taken r at a time.
The number of such combinations is denoted by:c(n,r)=n!/(r!*(n-r)!) in which n! is equal to n*(n-1)*(n-2).......*2*1
Example : In a conference of 9 schools, how many intraconference football games are played during the season if the teams all play each other exactly once?
When the teams play each other, order does not matter, we are counting match ups. For each game there is a group of two teams playing. So we can use combinations to help us out here.
First we need to find n and r :
If n is the number of teams we have to choose from, what do you think n is in this problem?
If you said n = 9 you are correct!!! There are 9 teams in the conference.
If r is the number of teams we are using at a time, what do you think r is?
If you said r = 2, pat yourself on the back!! 2 teams play per game.
Let's put those values into the combination formula and see what we get:
c(9,2)=9*8/2=36
so in the problem you shared we can say that for shaking hands we need 2 persons and these 2 persons are chosen among the 7 persons at that meeting.here it doesn't differ that the person number 1 shakes hands with the number 2 or number 2 shakes hands with number 1.so order is not important here.so we can use Combination here.the answer will be:
c(7,2)=7!/5!*2!=7*6/2=21
Replies
Thanx alot for all these information . I hate maths coz of my ego teacher in secondary school
Anyway .. Thats realy nice friend
Have anice day
Zahra said:
a part of Algebra in mathematics is related to solving of these kinds of problems which is called Combination:An arrangement of r objects,WITHOUT regard to ORDER and without repetition,selected from n distinct objects is called a combination of n objects taken r at a time.
The number of such combinations is denoted by:c(n,r)=n!/(r!*(n-r)!) in which n! is equal to n*(n-1)*(n-2).......*2*1
Example : In a conference of 9 schools, how many intraconference football games are played during the season if the teams all play each other exactly once?
When the teams play each other, order does not matter, we are counting match ups. For each game there is a group of two teams playing. So we can use combinations to help us out here.
First we need to find n and r :
If n is the number of teams we have to choose from, what do you think n is in this problem?
If you said n = 9 you are correct!!! There are 9 teams in the conference.
If r is the number of teams we are using at a time, what do you think r is?
If you said r = 2, pat yourself on the back!! 2 teams play per game.
Let's put those values into the combination formula and see what we get:
c(9,2)=9*8/2=36
so in the problem you shared we can say that for shaking hands we need 2 persons and these 2 persons are chosen among the 7 persons at that meeting.here it doesn't differ that the person number 1 shakes hands with the number 2 or number 2 shakes hands with number 1.so order is not important here.so we can use Combination here.the answer will be:
c(7,2)=7!/5!*2!=7*6/2=21
you can visit http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col... if you like to learn more.
the proof is as my friends stated.combination just simplifies your answering
thanks and have a nice time:)
Thanx dear for your comments
Keep smiling
I did it with some thinking ...
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