Combinations and Permutations
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Key Questions

Answer:
See below:
Explanation:
A combination is a grouping of distinct objects without regard to the order in which the grouping is made.
As an example, a poker hand is a combination  we don't care in what order we're dealt the cards, only that we're holding a Royal Flush (or a pair of 3s).
The formula for finding a combination is:
#C_(n,k)=((n),(k))=(n!)/((k!)(nk)!)# with#n="population", k="picks"# As a for instance, the number of possible 5card poker hands is:
#C_(52,5)=(52!)/((5)!(525)!)=(52!)/((5!)(47!))# Let's evaluate it!
#(52xx51xxcancelcolor(orange)(50)^10xx49xxcancelcolor(red)48^2xxcancelcolor(brown)(47!))/(cancelcolor(orange)5xxcancelcolor(red)(4xx3xx2)xxcancelcolor(brown)(47!))=52xx51xx10xx49xx2=2,598,960# 
Permutation involves arrangements whereas combination implies number of selections or combinations.
Number of permutations of three letters from given five letters a, b, c, d, e is 60 as follows
abc,acb,bac,bca,cab,cba
abd,adb,bad,bda,dab,dba
abe,...
acd,..
ace,...
ade,...
bcd,..
bce,...
bde,...
cde,...
10 x 6 = 60
now number of combinations of five letters a,b,c,d,e taken three at a time is just ten, namely
abc,abd,abe,acd, ace,ade, bcd,bce, bde, cde. 
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