Difference between permutation and combination
Before solving any question related to permutation and combination, it is necessary to know the difference between permutation and combination. Students should be very clear about when to use permutation and when to use combination.
Let's see two cases to have a clear understanding of permutation and combination
Case 1: In a racing competition there are 6 participants and we have to find the total number of ways in which 3 medals (gold, silver and bronze) can be won.
Now whether it is a question of permutation or combination. we have to think about whether order matters or not. If a participant comes first he will get gold, if he comes second he will get silver and if he comes third he will get bronze. It means order matter here. So, it is a question of permutation.
Case 2: In a school racing team we have to select 3 racers and there are 6 participants in how many ways these 3 racers can be selected.
Now again to know whether is it a question of permutation or combination, think whether order matter or not. So, if a participant comes first off course he will be selected. Similarly, the participants who come 2nd and 3rd, they will also get selected. So, in this question, top 3 will get selected it doesn't matter that in which order they are finishing the race. In other words, we have to select the top 3 racers out of 6 participants. So, it is a problem of combination.
In case 1 we have to find the total number of permutation for 3 medals from 6 participants.
n= 6, r= 3
Here, we have to find the value of 6P3.
C(6,3)=6!(6 -3)!=
= 6⋅5⋅4⋅3⋅2⋅13⋅2⋅1
In case 2 we have to find the total number of combination for selecting 3 winners from 6 participants.
n=6, r= 3
Here, we have to find the value of 6C3.
C(6,3)=6!3! (6 -3)!=
= 6⋅5⋅4⋅3⋅2⋅1(3⋅2⋅1)(3⋅2⋅1)
It means there is a total of 20 ways of selecting 3 runners out of 6 runners.
I hope now you know the difference between permutation and combination along with the approach to solving the question.
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Also, do not forget to give your feedback in the comment section, your feedback is most important to me.
Difference between permutation and combination
In permutation order of the objects matters whereas in the combination order of the objects doesn't matter.Let's see two cases to have a clear understanding of permutation and combination
Case 1: In a racing competition there are 6 participants and we have to find the total number of ways in which 3 medals (gold, silver and bronze) can be won.
Now whether it is a question of permutation or combination. we have to think about whether order matters or not. If a participant comes first he will get gold, if he comes second he will get silver and if he comes third he will get bronze. It means order matter here. So, it is a question of permutation.
Case 2: In a school racing team we have to select 3 racers and there are 6 participants in how many ways these 3 racers can be selected.
Now again to know whether is it a question of permutation or combination, think whether order matter or not. So, if a participant comes first off course he will be selected. Similarly, the participants who come 2nd and 3rd, they will also get selected. So, in this question, top 3 will get selected it doesn't matter that in which order they are finishing the race. In other words, we have to select the top 3 racers out of 6 participants. So, it is a problem of combination.
After knowing the difference between permutation and combination, Next thing is to understand the formula of permutation and combination.
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| Permutation and combination difference |
The number of permutations of n objects taken r at a time is determined by the formula of nPr. Whereas number of the combination of n objects taken r at a time is given by the nCr.
In case 1 we have to find the total number of permutation for 3 medals from 6 participants.
n= 6, r= 3
Here, we have to find the value of 6P3.
C(6,3)=6!(6 -3)!=
= 6⋅5⋅4⋅3⋅2⋅13⋅2⋅1
= 120
It means there is a total of 120 number of ways in which 3 medals can be won by 6 participants.
n=6, r= 3
Here, we have to find the value of 6C3.
C(6,3)=6!3! (6 -3)!=
= 6⋅5⋅4⋅3⋅2⋅1(3⋅2⋅1)(3⋅2⋅1)
= 20
It means there is a total of 20 ways of selecting 3 runners out of 6 runners.
I hope now you know the difference between permutation and combination along with the approach to solving the question.
Please like, share and subscribe to my blog.
Also, do not forget to give your feedback in the comment section, your feedback is most important to me.
Difference between permutation and combination
Reviewed by goodinfo
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November 16, 2019
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Reviewed by goodinfo
on
November 16, 2019
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