0 votes 0 votes I thought it is multi set, each of the 4 places have 6 choices. so 64 . .?? please clear this out. What is multiset means?? atul_21 asked Dec 22, 2017 atul_21 430 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply joshi_nitish commented Dec 23, 2017 i edited by Tesla! Dec 23, 2017 reply Follow Share when you are doing 64, you can come up with two sets as shown below, {1 , 2, 4, 4} and {4, 4, 1 ,2} though in multisets duplicates are allowed but oreder does not matter in multisets also. you can find out like this, CASE1: all four are different (eg: {1,3,4,5}) -> $\binom{6}{4}$ = 15 CASE2: one pair of same another pair of different (eg:{1,1,2,4}) -> $\binom{6}{3}$*3 = 60 CASE3: two pairs of same (eg: {1,1,3,3}) -> $\binom{6}{2}$ = 15 CASE3: three same and one different (eg: {1,1,1,4})-> $\binom{6}{2}$*2 = 30 CASE4: all same (eg: {2,2,2,2}) -> $\binom{6}{1}$ = 6 adding all up, you will get 126. 3 votes 3 votes atul_21 commented Dec 23, 2017 reply Follow Share Please explain how it is "CASE2: one pair of same another pair of different (eg:{1,1,2,4}) -> (6C3)*3 = 60" ???? Why multiply with 3???? 0 votes 0 votes joshi_nitish commented Dec 23, 2017 reply Follow Share i will show with reference to this set, {1,1,2,4},.....first select any 3 elements(i.e 1,2,4) in $\binom{6}{3}$ then any one among these 3 can be duplicate(i.e 1,1).. so total $\binom{6}{3}$*3 ways for performing CASE2 1 votes 1 votes atul_21 commented Dec 23, 2017 reply Follow Share ok thanx a lot :) (was not getting this simple thing) Make ur cmment as answer 0 votes 0 votes Please log in or register to add a comment.
Best answer 0 votes 0 votes The genrating function for this : (1+x+x2+x3+x4+x5+ . . . .)6 Coefficient of x4 in: (1-x)-6 = 1+6C1 x + 7C2 x2 +. . . = 9C4 = 126 atul_21 answered Dec 23, 2017 atul_21 comment Share Follow See all 0 reply Please log in or register to add a comment.