There are $n$ types of different articles. The names of the types are - $A_1,A_2,A_3,...,A_n$ Number of article $A_1$ is $B_1$ , $A_2$ is $B_2$... same goes upto $A_n$. We have to choose k articles.Repetition is allowed.
A colorful version would be something like this- You go to a bakery,you need to buy k cakes.You see that there are n types of cakes ie. chocolate,vanilla,mango,pineapple,orange etc.. and also notice that there are only c chocolate cakes,v vanilla cakes,m mango cakes,p pineaple cakes and so on.In how many ways can you buy k cakes when you don't take order into concern?