a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 9 managers , if 3 managers will not attend the meeting together .
"9 managers , but 3 of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these 3 managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the 3 managers . select 1 manager from 3 , and then select 4 from the remaining 6 , which is 3 c 1 + 6 c 4 = 18 + 6 = 24 . answer : a"
subtract(choose(9, 5), choose(subtract(9, 3), 3))