2 votes 2 votes Consider all possible permutations of eight distinct elements $a, b, c, d, e, f, g, h$. In how many of them, will $d$ appear before $b$? Note that $d$ and $b$ may not necessarily be consecutive. Combinatory descriptive isi2015-pcb-a combinatory + – go_editor asked May 29, 2016 • retagged Jun 27, 2017 by Arjun go_editor 698 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes 8!/2! as (d,b) is the only permitted arrangement between d and b , so it is equivalent to treating them as similar objects. Prasita Mukherjee answered May 29, 2016 Prasita Mukherjee comment Share Follow See 1 comment See all 1 1 comment reply Debasmita Bhoumik commented May 8, 2018 reply Follow Share d,b is not the only arrangement. d,a,c,b is also permitted. consecutive not necessary 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes d should be placed before b. answer in pic (courtesy: friend) Debasmita Bhoumik answered May 8, 2018 Debasmita Bhoumik comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes If d is at position 1, then total permutations = 7! if d is at position 2 = choices for placing b * permutation of remaining objects = 6 * 6! if d is at position 3 = 5 * 6! similarily, for pos = 4, total permutations = 4 * 6! for pos = 5, total permutations = 3 * 6! for pos = 6, total permutations = 2 * 6! for pos = 7, total permutations = 1 * 6! => total permutations = 6!(7 + 6 + 5 + 4 + 3 + 2 + 1) = 6! * 28 neeraj_bhatt answered Sep 6, 2020 neeraj_bhatt comment Share Follow See all 0 reply Please log in or register to add a comment.