stats

[LAKSHITA JAIN]

A shelf contains six seperate compartments.in how many ways can four indistinguishable marbled be placed in compartment so that no compartment is empty.??

[anon_econ]

Umm zero bcoz all 6 have to have at least 1 marble but we have only 4 marbles..?

[manvi ahuja]

Oh sry...number of marbles are twelve not four

[anon_econ]

Let xi be the number of marbles in the ith compartment. Then u have to find out the number of positive integer solutions of x1+x2+x3+x4+x5+x6=12. To know how to find this, see this: http://www.askiitians.com/iit-jee-algebra/permutations-and-combinations/derangements-and-multinomial-theorem.aspx

[kratika]

i think it should be the positive integer solutions for x1+x2+x3+x4+x5+x6=6 because we have to assign atleast one marble to each of the 6 compartment so we will deduct that from total number 12 and arrange the remaining 6

[anon_econ]

In that case u will have to find out the number of non-negative integer solutions, rather than positive integer solutions (bcoz xi can be =0). That will give u the same answer.