1 1 vote How many non – negative integral solutions are there to the equation $x_1 + x_2 + x_3 + x_4 + x_5 = 40$ if we must satisfy $x_1 \leq 20$ ? Mathematical Logic discrete-mathematics combinatory + – atul_21 2.2k views answer comment Share Follow Print See all 8 Comments 8 8 Comments reply Anu007 commented Dec 22, 2017 reply Follow flag 40+5-1C4 - 19+5-1C4 1 1 replyShare atul_21 commented Dec 22, 2017 reply Follow flag https://www.andrew.cmu.edu/course/15-251/Recitations/recitation03/rec03_sol.pdf page no.2 please explain me,if u get it 0 0 replyShare atul_21 commented Dec 22, 2017 reply Follow flag Anu007 Exactly it must be this. but see the link. I think its wrong there? what do u think? 0 0 replyShare Anu007 commented Dec 22, 2017 reply Follow flag total - 21<= i think like that 1 1 replyShare atul_21 commented Dec 22, 2017 reply Follow flag Yes ur approach is absolutely correct 0 0 replyShare hs_yadav commented Dec 22, 2017 reply Follow flag @ Anu007 i think there is need some modification in your solution.....it would be like this....i think 44C40 - 5* 23C19 0 0 replyShare Shubhanshu commented Dec 22, 2017 reply Follow flag @hs_yadav x<= 20 condition is applicable only on x1 not on all. x1 ≤ 20 0 0 replyShare hs_yadav commented Dec 23, 2017 reply Follow flag yup ...:) thank u sir... 0 0 replyShare Please log in or register to add a comment.
Best answer 2 2 votes (:........:) #edited 0<=x<=20 non-negative solution is equal to the value of coefficient of x40 in following expression... (1+x+x2+x3+x4+x5+.......+x20)(1+x+x2+x3+x4+x5+.......+x40)4 :- (1-x21) (1-x41)4 (1-x)-5 ..:- (1-x21) *4C0 * (1-x)-5 :- coefficient of x40 in 1* (1-x)-5 +coefficient of x40 in -x21 * (1-x)-5 :- 40+5-1C40 - 19+5-1C19 :- 44C40 - 23C19 hs_yadav answered Dec 22, 2017 • selected Dec 23, 2017 by atul_21 hs_yadav comment Share Follow See all 3 Comments 3 3 Comments reply atul_21 commented Dec 23, 2017 reply Follow flag How the generating function is this??? Only x1 <= 20 , others can be anywhere in between 0-40 . .. Are u getting it?? 1 1 replyShare hs_yadav commented Dec 23, 2017 reply Follow flag @ atul_21 now it's ok(edited)...thanks... 0 0 replyShare atul_21 commented Dec 23, 2017 reply Follow flag #perfect @hs_yadav 0 0 replyShare Please log in or register to add a comment.
