The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students are to be selected at random from the class, (a) how many different groups of seven students can be selected? (b) how many different groups of seven students consist entirely of freshman?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students are to be selected at random from the class,
(a) how many different groups of seven students can be selected?
(b) how many different groups of seven students consist entirely of freshman?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
