In: Math
1a)Out of the 50 candidates in the question above, 28 are women
and 22 are
men. How many ways can the committee of 12 be randomly chosen where
7 members
are women and 5 members are men?
b) In a group of students, each student is taking a mathematics
course or a
computer science course or both. One-fifth of those taking a
mathematics course are
also taking a computer science course, and one-sixth of those
taking a computer science
course are also taking a mathematics course. What percentage of the
students
are taking a mathematics course?
c) A coin is flipped 10 times. How many outcomes have exactly 3 heads?
d) Three committees of 5, 10, and 15 are to be chosen out of a
total of 30. How
many ways can the committee be formed?