In an exam, a student is required to answer 10 out of 13 questions. Find the number of possible choices if the student must answer: (a) the first two questions; (b) the first or second question, but not both; (c) exactly 3 out of the first 5 questions; (d) at least 3 out of the first 5 questions
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.
In an exam, a student is required to answer 10 out of 13 questions. Find the number of possible choices if the student must answer:
(a) the first two questions;
(b) the first or second question, but not both;
(c) exactly 3 out of the first 5 questions;
(d) at least 3 out of the first 5 questions.
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