4 votes 4 votes There are three divisions of employees and each category has $5$ employees. The total number of ways a team of $8$ employees can be formed (where at least $2$ members from each division must be included in the team) is _________. Mathematical Logic tbb-mathematics-2 numerical-answers + – Bikram asked May 24, 2017 edited Aug 14, 2019 by Counsellor Bikram 438 views answer comment Share Follow See 1 comment See all 1 1 comment reply bhuv commented Jan 9, 2018 reply Follow Share Can we solve this by X1+X2+X3=8 n+r-1Cr anyway? 0 votes 0 votes Please log in or register to add a comment.
Best answer 4 votes 4 votes (3,3,2)(3,2,3)(2,3,3)(4,2,2)(2,4,2)(2,2,4) ways and count them using combinations Bikram answered May 24, 2017 selected Jun 6, 2017 by srestha Bikram comment Share Follow See all 4 Comments See all 4 4 Comments reply Harsh181996 commented Jun 2, 2017 reply Follow Share Sir, I understood what you did above but , I solved using the following approach - Select two members from each group which is 5C2 * 5C2 *5C2. Now we have remaining 9 people in total left . Now there is no restriction on to fill the remaining two spots - there are 9 choices * 8 choices. Final Answer - 5C2 * 5C2 *5C2 * 9 *8 It comes out to be very different 1 votes 1 votes Hemant Parihar commented Jun 4, 2017 reply Follow Share @Harsh, In our counting there is redundancy. Suppose in our first set {1, 2, 3, 4,5 } these element present. You are selecting first two element suppose you select {1, 2 } . Now after selecting 4 element from other two set. 9 people are left. No restricted is there. So you are selecting 2 people from these 9. Suppose you select 3. 4. So from the first set you select {1, 2, 3, 4}. Now think, When you are picking two element, you might pick {3, 4}. Now again select 4 element from other two set. Suppose that these element are same 4 element that you have select for above one. Now again 9 people are left. No restriction. We select from these 9. {1, 2} Now again from the first set we select {1,2,3, 4}. 6 votes 6 votes Sachin Tripathi commented Jun 9, 2017 reply Follow Share If we consider these three divisions as three objects (variables)and every object is positive (>=0) X1+X2+X3=8 Than it can be solved as n+r-1Cr But how to include atleast 2 thing in it 0 votes 0 votes bhuv commented Jan 9, 2018 reply Follow Share @bikram sir why after getting number of ways as 6 you took combinations of those? I didn't get that part. Was that because you were considering employees as distinct, if we consider them indistinguishable from each other in there category then this problem reduce to like three type of donuts and we need have a combination of 8 with atleast 2 each of them, which give us answer as 6 way possible. But if now we consider each donut having different colour, then how many different colour combinations of such 8 donuts possible with given conditions, then your answer is correct. Tell me if I have done some mistake. 0 votes 0 votes Please log in or register to add a comment.