0 votes 0 votes Number of ways to distribute 5 distinct toys to 3 children A,B,C such that each one of them gets atleast one toy. My answer come to be 75.Is it correct? Also, when toys are not distinct, will answer change? Combinatory combinatory discrete-mathematics + – Ayush Upadhyaya asked Aug 29, 2018 Ayush Upadhyaya 494 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Deepanshu commented Aug 29, 2018 reply Follow Share @MiNiPanda I AM ALSO DOING LIKE THE SOLUTION BELOW 0 votes 0 votes Deepanshu commented Aug 29, 2018 reply Follow Share BUT 144 NOT 150 0 votes 0 votes Lakshman Bhaiya commented Oct 24, 2018 reply Follow Share i'm get $147$ 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Each toy can be given to one of the three children: 35 Subtract the number of ways atleast one child is not given a toy from total outcomes. Using inclusion exclusion 35 -(3C1*25 - 3C2*15) =150 Another approach As @MiniPanda said the problem can be considered as how many onto functions are there from a set of 5 to a set of 3. sakharam answered Aug 29, 2018 • edited Aug 29, 2018 by sakharam sakharam comment Share Follow See all 2 Comments See all 2 2 Comments reply Ayush Upadhyaya commented Aug 30, 2018 reply Follow Share Okay. And when toys are not distinct, the answer is 75 right? 0 votes 0 votes sakharam commented Aug 31, 2018 reply Follow Share If toys are not distinct then, WAY 1 c1+c2+c3=5 Since each child gets atleast one toy: c1+c2+c3=2 Using stars and bars technique ( https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)) 2+3-1C2 =4C2=6 OR WAY 2 Child1 Child 2 Child 3 1 1 3 1 3 1 3 1 1 2 2 1 2 1 2 1 2 2 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes The answer is the Stirling number of the second kind. Read more here: https://math.stackexchange.com/questions/1495278/choosing-distinct-balls-to-put-into-indentical-urns https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind goxul answered Aug 29, 2018 goxul comment Share Follow See all 0 reply Please log in or register to add a comment.