A student s to answer 10 out of 13 questions in an exam. How many choices he has if he must answer at least 3 of the first 5 questions.

Answer 1

Assuming that he can answer them in any order and that he is not restricted to anwering only 3 of the first 5, that is, he could answer all of the first five.
step one: number of ways to answer the obligatory questions = C(5,3) = 10
So now he has to answer 7 more of any of the remaining 10
= C(10,7) = 120

number of ways = 12(120) = 1200

Answer 2

a women student is to answer b10 out of 13 questions.find the number of her choices where she must answer
a,the frist two question
b,exactly 3 out of the frist 5 question
c,the first or second question but not both;
at least3 of the frist 5 question