6 votes 6 votes The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $$ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $$ In how many different ways can one do this if the piles are also distinguishable? Combinatory goclasses2024-mockgate-12 goclasses numerical-answers combinatory counting 1-mark + – GO Classes asked Jan 21 • retagged Jan 25 by Lakshman Bhaiya GO Classes 1.0k views answer comment Share Follow See 1 comment See all 1 1 comment reply GO Classes Support commented Jan 25 reply Follow Share $ \large{\colorbox{yellow}{Detailed video solution of this question with direct time stamp}}$ All India Mock Test 3 - Solutions Part 1 1 votes 1 votes Please log in or register to add a comment.
6 votes 6 votes Ans: $3! \cdot 9330=55980$ An algorithm to create such a distribution is by first dividing the objects over three indistinguishable non-empty piles, which can be done in $9330$ ways. After that, we can put three different labels on the three piles, which can be done in $3 !=6$ ways. So in total, there are $6 \cdot9330$ ways to divide the objects over the piles. GO Classes answered Jan 21 • edited Jan 21 by Lakshman Bhaiya GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Let Object Set = O = {O1,O2,O3,……..O10} Let Pile Set = P = {P1, P2, P3} distribution of object in to given piles is nothing but no of onto function from Object Set to Pile Set, Which is, 3^10 – 3C1 * 2^10 + 3C2 * 1^10 = 55980 krishnajsw answered Jan 21 krishnajsw comment Share Follow See 1 comment See all 1 1 comment reply Philosophical_Virus commented Jan 23 reply Follow Share great approach 🔥 1 votes 1 votes Please log in or register to add a comment.
