0 votes 0 votes There are total 21 identical balls in a shop and 7 children. In how many ways can 7 children claim the balls? (it is not necessary to claim all the balls) Combinatory combinatory + – Mk Utkarsh asked Mar 3, 2018 Mk Utkarsh 1.4k views answer comment Share Follow See all 9 Comments See all 9 9 Comments reply srestha commented Mar 3, 2018 reply Follow Share $\binom{21+7-1}{7-1}$ $=\binom{27}{6}$ 0 votes 0 votes Mk Utkarsh commented Mar 3, 2018 reply Follow Share srestha those are the cases where all balls are picked we can even pick only 2 balls 0 votes 0 votes air1 commented Mar 3, 2018 reply Follow Share @Mk Utkarsh Distributing $<= K$ items to $N$ persons is same as distributing exactly $K$ items to $N+1$ persons. 3 votes 3 votes srestha commented Mar 3, 2018 reply Follow Share yes otherwise problem will be unsolvable 0 votes 0 votes Mk Utkarsh commented Mar 3, 2018 reply Follow Share so answer will be $\binom{28}{7}$ 2 votes 2 votes Mk Utkarsh commented Mar 3, 2018 reply Follow Share air1 i agree it is because we assume a virtual child who picks up the number of balls no other kid picked up so that's why it works :) 1 votes 1 votes air1 commented Mar 3, 2018 reply Follow Share Yes. 0 votes 0 votes Balaji Jegan commented Mar 3, 2018 reply Follow Share I agree with Shrestha's answer. You have to use Formula 5. 0 votes 0 votes Balaji Jegan commented Mar 3, 2018 reply Follow Share In case, all the children are Dopple Gangers or Septuplets, then use Formula 13 0 votes 0 votes Please log in or register to add a comment.