1 votes 1 votes #discrete 6 runners are in a 100 yard dash. Find the ways possible for 3 medals to be awarded if ties are possible. Mathematical Logic discrete-mathematics combinatory + – nick17india asked May 5, 2017 retagged Jun 27, 2017 by Arjun nick17india 541 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Here ties are possible and runner position depends on how many runner ahead of him finish the race and also one medal can be awarded to more than one person if there is a tie. when there is one person for 1st position ,one for 2nd position and more than one for 3rd position. : 6c1 * 5c1 * (4c1 + 4c2 + 4c3 + 4c4 ) = 450 when there is one person for 1st position and more than one person for 2nd position in that case there is no person at 3rd position (bcoz already 3 are ahead of them) : 6c1 * ( 5c2 + 5c3 + 5c4 +5c5 ) = 156 if there is two person for 1st position then there is no person for 2nd position and at 3rd position can be more than one person : 6c2 * ( 4c1 +4c2 +4c3 +4c4 ) = 225 if there is more than two person for 1st position then there is no one at place 2nd or 3rd : ( 6c3 + 6c4 + 6c5 +6c6 ) =42 summing all of them is equal to 873 ANKUSH KUMAR answered May 5, 2017 ANKUSH KUMAR comment Share Follow See all 2 Comments See all 2 2 Comments reply papesh commented May 6, 2017 reply Follow Share why it is not possible that the first medal is given to 3 people, second one to 2 persons, and remaining can get the third medal ?? 0 votes 0 votes ANKUSH KUMAR commented May 6, 2017 i edited by ANKUSH KUMAR May 6, 2017 reply Follow Share if there is 3 people at first position then no one can be second or third bcoz already 3 person are ahead of them. now the next person is at position 4 ( position is decided by how many runner ahead of him finish the race ). 0 votes 0 votes Please log in or register to add a comment.