Permutation(arrangement of objects):
The number of permutations of n distinct objects, taken r at a time, is the total number of arrangements of r elements, chosen from n objects where the order of the arrangement is very important. Arranging n different objects, taken r at a time is similar to filling r places from n objects.
r-Places: |
|
Number of Choices:
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n n - 1 n - 2 (n - r-1) |
The number of types of arranging = The number of types of filling r places
(b) The number of arrangements of n separate things taken all at a time =npn= n!
Combination:
Meaning of combination is choice of objects.
选择的对象without repetition:
The number of choices (combinations or groups) that may be created from n different objects taken r (0 ≤ r ≤ n) at a time is
选择的对象with repetition:
The number of combinations of n different objects, taken r at a time when each can occur once, twice, thrice,..... upto r times in any combination isnHr=n+r-1Cr.
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