(b) A tea party is arranged for 16 persons along two sides of a table with 8 chairs
on each side. 4 persons wish to sit on on particular side and 2 on the other
side. In how many ways can they be seated? (
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Permutation is when order matters, combination is when order does not matter
They are concepts used in probability theory.
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.
N!/N
The "combination" for a lock is actually a permutation, an ordered sequence. So for example: 1,2,3 and 3,2,1 are the same combination, but a different permutation. When opening a lock, obviously the sequence is important, so we want to calculate the permutations. To do that, you multiply the number of possible choices for the first position times the number of possible choices for the second position, etc. Assuming that you can use the same number in all three positions (so 60 to the left, 60 to the right and 60 to the left is a valid choice), there are 60 x 60 x 60 possible permutations, or "combinations" for the lock = 216,000. If you were not allowed to use the same number twice, it would be 60 x 59 x 58 = 205,320. If you could repeat the same number, but not in sequence (so 20, 30, 20 is OK; but 20, 20, 30 is not), then there would be 60 x 59 x 59 = 208,860.