0 0 votes The total number of ways in which 5 balls of different color can be distributed among 3 persons so that each person gets at least one ball is: Mathematical Logic combinatory + – Rackson 1.2k views answer comment Share Follow Print See all 3 Comments 3 3 Comments reply Satbir commented Feb 14, 2019 i edited by Satbir Feb 14, 2019 reply Follow flag 150 ? 0 0 replyShare ck commented Feb 14, 2019 reply Follow flag 13? 0 0 replyShare Swapnil Naik commented Feb 14, 2019 reply Follow flag http://clay6.com/qa/12342/the-total-no-of-ways-in-which-5-balls-of-different-colours-can-be-distribut 2 2 replyShare Please log in or register to add a comment.
Best answer 0 0 votes This is similar to total number of onto functions from m elements to n elements. $\sum_{k=0}^{n}(-1)^{k}$ $^{n}C_{k}(n-k)^{m}$ Given m=5 and n=3 $\therefore$ The total number of ways in which 5 balls of different color can be distributed among 3 persons so that each person gets at least one ball is = $3^{5}-$ $^{3}C_{1}(3-1)^{5}+$ $^{3}C_{2}(3-2)^{5}-$ $^{3}C_{3}(3-3)^{5}$ = 243 - 32*3 + 3 - 1 =243 - 93 =150 Satbir answered Feb 14, 2019 • selected Feb 14, 2019 by Rackson Satbir comment Share Follow 0 reply Please log in or register to add a comment.
