Question Number 102243 by mathocean1 last updated on 07/Jul/20

At examination, a student most answer to 8 question betwen a total of 10 question. 1) How many many choices is possible? 2)How many choices is possible if a student most answer to 3 questions at least? 3)How many choices is possible if a student most answer to at least 4 questions of the five first questions?

Answered by mr W last updated on 07/Jul/20

1) to select 8 from 10 questions there are C_8 ^(10) =45 possibilities. 2) do you mean 3 certain questions must be selected? then one can select 5 from the remaining 7 questions, there are C_5 ^7 =21 ways. 3) to select at least 4 from the first 5 questions, there are C_4 ^5 ways, then select another 4 from the remaining 6 questions, there are C_4 ^6 ways, totally C_4 ^5 ×C_4 ^6 =75 ways.