What is the difference between permutation and combination?
Explain briefly.
Explain briefly.
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A Permutation is an ordered Combination.
If the order doesn't matter, it is a Combination.
If the order does matter it is a Permutation.
If the order doesn't matter, it is a Combination.
If the order does matter it is a Permutation.
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In a permutation, order is significant.
In a combination, order is not significant.
So if you have 10 cards numbered 1 to 10 and you draw this card sequence:
3, 5, 1, 9
As a permutation, it's different from drawing 9, 1, 5, 3 (which is another permutation of the same numbers). Two permutations are the same when they're identical as ordered k-tuples.
As a combination, it's not. Two combinations are the same when they're identical as sets.
In a combination, order is not significant.
So if you have 10 cards numbered 1 to 10 and you draw this card sequence:
3, 5, 1, 9
As a permutation, it's different from drawing 9, 1, 5, 3 (which is another permutation of the same numbers). Two permutations are the same when they're identical as ordered k-tuples.
As a combination, it's not. Two combinations are the same when they're identical as sets.
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Let's use an example similar to the lottery balls:
Combination gives you a number that is the possible ways that you can select some number (n) lottery balls from (m) lottery balls (where m > n) without repeating the same number on the ball.
Permutation gives you a number that is the possible ways that you can select some number (n) lottery balls from (m) lottery balls (where m > n) where repeating the same number on the ball is possible. (as if put each ball back in the machine after you recorded its number so that it could be drawn again).
Combination gives you a number that is the possible ways that you can select some number (n) lottery balls from (m) lottery balls (where m > n) without repeating the same number on the ball.
Permutation gives you a number that is the possible ways that you can select some number (n) lottery balls from (m) lottery balls (where m > n) where repeating the same number on the ball is possible. (as if put each ball back in the machine after you recorded its number so that it could be drawn again).