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.