In how many ways can 5 different marbles be distributed in 4 identical pockets? A - 24 B - 51 C - 120 D - 625 E - 1024 oa - B

faraz_jeddah wrote:In how many ways can 5 different marbles be distributed in 4 identical pockets? A - 24 B - 51 C - 120 D - 625 E - 1024 oa - B Case 1: All 5 marbles in 1 pocket. As all pockets are identical, no. of ways it can be done = 1 Case 2: 4 marbles in 1 plus 1 marble in another. Again, all pockets are identical, we just have to find no. of ways of choosing 1 marble out of 5 marbles = 5C1 = 5 Case 3: 3 marbles + 2 marbles, No. of ways = 5C2 = 10 Case 4: 1 + 1 + 3 No. of ways = Choose 3 out of 5 to form a group, other 2 can go in any pocket as pockets are all identical. = 5C3 = 10 Case 5: 1 + 2 + 2 Choose 1st out of 5: 5 ways Choose 2 out of 4: 4C2/2 = 3 ways. (Our of group of ABCD, choosing 2 has 6 ways, but in our case choosing AB or choosing CD are both same, so we have to divide it by 2.) Total = 5 X 3 = 15. Case 6: 1 + 1 + 1 + 2 Choose 2 of 5 = 5C2 = 10. TOTAL: 1 + 5 + 10 + 10 + 15 + 10 =51

mkdureja wrote:faraz_jeddah wrote:In how many ways can 5 different marbles be distributed in 4 identical pockets? A - 24 B - 51 C - 120 D - 625 E - 1024 oa - B Case 1: All 5 marbles in 1 pocket. As all pockets are identical, no. of ways it can be done = 1 Case 2: 4 marbles in 1 plus 1 marble in another. Again, all pockets are identical, we just have to find no. of ways of choosing 1 marble out of 5 marbles = 5C1 = 5 Case 3: 3 marbles + 2 marbles, No. of ways = 5C2 = 10 Case 4: 1 + 1 + 3 No. of ways = Choose 3 out of 5 to form a group, other 2 can go in any pocket as pockets are all identical. = 5C3 = 10 Case 5: 1 + 2 + 2 Choose 1st out of 5: 5 ways Choose 2 out of 4: 4C2/2 = 3 ways. (Our of group of ABCD, choosing 2 has 6 ways, but in our case choosing AB or choosing CD are both same, so we have to divide it by 2.) Total = 5 X 3 = 15. Case 6: 1 + 1 + 1 + 2 Choose 2 of 5 = 5C2 = 10. TOTAL: 1 + 5 + 10 + 10 + 15 + 10 =51 So since it mentions identical bags, there is no difference between choosing 4 then 1 and choosing 1 then 4. Correct?