Question 530246:  Danny, Connie, and Jane have eight cookies to share among themselves. They decide that they each do not need to get the same number of cookies, but each person should get at least one cookie. If the children do not break any of the cookies, in how many different ways can they share the cookies? 
 Answer by sudhanshu_kmr(1152)      (Show Source): 
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8 cookies to share among 3 persons, but each person should get at least one.
 
so, after giving one to all 3 persons, there are 5 to share among 3. 
 
5+3-1 = 7
 
3-1 = 2
 
number of ways = 7C2 = 21
 
 
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