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When we use permutation or combination?
Permutation is when order matters, combination is when order does not matter
Permutation combination?
They are concepts used in probability theory.
Why are the answers from a permutation bigger than from a combination?
Because a permutation includes all the different arrangements or order of the items in a set. In a combination the order doesn't matter or count.
How do you solve a permutation in math?
If there are n objects to fit r places (e.g. 9 people in 7 chairs, 4 tumblers in a lock) then the number of permutations is nCk, stated as n-choose-k. This number can be calculated by the formula n!/(n - k)!. If k is equal to n, then (n - k)! = 0! = 1, and the number of permutations is simply n!. If the direction of the permutation is irrelevant (e.g. ABCD is the same as DCBA) then divide by two to cancel out the double-counting.
How do you prove a Ring to be commutative?
To prove a ring is commutative, one must show that for any two elements of the ring their product does not depend on the order in which you multiply them. For example, if p and q are any two elements of your ring then p*q must equal q*p in order for the ring to be commutative. Note that not every ring is commutative, in some rings p*q does not equal q*p for arbitrary q and p (for example, the ring of 2x2 matrices).
