Let the sample space beUpper S equals StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 EndSet
S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.Suppose the outcomes are equally likely. Compute the probability of the eventUpper E equals StartSet 1 comma 2 comma 4 comma 6 EndSetE={1, 2, 4, 6}.
We know that the number of combinations of n things taking r at a time is given by :-
Given : Total multiple-choice questions = 9
Total open-ended problems=6
If an examine must answer 6 of the multiple-choice questions and 4 of the open-ended problems ,
No. of ways to answer 6 multiple-choice questions
=
No. of ways to answer 4 open-ended problems
=
Then by using the Fundamental principal of counting the number of ways can the questions and problems be chosen = No. of ways to answer 6 multiple-choice questions x No. of ways to answer 4 open-ended problems