Answer with Step-by-step explanation:
Permutation : It is an arrangement of r elements out of n elements.
Combination : it is a selection of r element out of n elements .
Suppose we have a set
S={1,2,3}
If two elements are taken at a time then
Using permutation formula
Total number of outcomes=[tex]3P_2[/tex]
Total number of outcomes=[tex]\frac{3!}{(3-2)!}[/tex]
Total number of outcomes=3!=[tex]3\times 2\times1=6[/tex]
Using combination formula
[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex]
Total number of outcomes=[tex]\binom{3}{2}=\frac{3!}{2!1!}[/tex]
Total number of outcomes=[tex]\frac{3\times2!}{2!}[/tex]
Hence, total number of outcomes=3
Total number of outcomes determined by permutation have more outcomes.
Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements
Arrangements of two elements out of 3 elements
{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}
By using combination if two elements taken at a time then combination
{1,2},{2,3},{1,3}
