2 votes 2 votes How many ways are there to distribute 10 balls into 6 boxes with atmost 4 balls in first 2 boxes if the balls are in distinguishable? Combinatory combinatory + – srestha asked Jan 7, 2018 srestha 511 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments srestha commented Jan 9, 2018 reply Follow Share if this question is for distinguishable, what will be ur answer? 0 votes 0 votes Mk Utkarsh commented Jan 9, 2018 reply Follow Share lets name the balls with A,B,C,D,E,F,G,H,I,J and Boxes with X1,X2,X3,X4,X5,X6 total number of combinations = 610 (total number of balls = 10 and total number of options a ball can go = 6) let A be the set of combinations with X1 > 4 balls total combinations will be = 10C5 * 55 (remaining 5 balls will have 5 options to go so 5 x 5 x 5 x 5 x 5 = 55) let B be the set of combinations with X2 > 4 balls total combinations will be = 10C5 * 55 by inclusion exclusion, |A| + |B| - |A ∩B| lets calculate |A ∩ B|, X1 , X2 > 4 |A ∩ B| = 10C5 * 5C5 |A $\cup$ B| = 2 ( 10C5 * 55 ) - 10C5 * 5C5 |A $\cup$ B| = 157478 Total combinations - |A $\cup$ B| = 610 - 157478 = 60308698 0 votes 0 votes Mk Utkarsh commented Jan 9, 2018 reply Follow Share I don't know why i named the balls 0 votes 0 votes Please log in or register to add a comment.