Distinct arrangement of n number of  objects among  r distinct cells (without ordering inside a cell)

 Value of     n Value of     r Value of p things excluded/included Each cell to contain at least q objects Partition arrangements (maximum 5) ----

* q1 objects are of 1 type, q2 of another type, q3 another type & sum of (q1+q2+....qn)=n. Here we take upto 5 types in the row "Partition arrangements"

 When Objects are indistinguishable from one another Description Formulae Each cell can have one or more objects or can be empty n+r-1Cn Each cell can have one  object or empty (r => n) r! / [n!(r-n)!] Each cell to have at least one object but not empty n-1Cr-1 Each cell to have at least q objects n+r-1-rqCr-1 distribution of q1,q2,q3,...qn* objects aggregating n & n<=r [r! / (q1!q2!q3!...qn)][1/(r-n)!] Arrangement with distribution as per partition n! / (n1!n2!n3!n4!n5!) When Objects are distinguishable from one another Description Formulae Each cell can have one or more objects or can be empty (n 0) -nCr = (-1)r[n+r-1Cr]