In an examination,there are three multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is:

In a football championship,there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is

Consider the set of all triangles $OPQ$ where $O$ is the origin and $P$,$Q$ are distinct points in the plane with non-negative integral coordinates $(x, y)$ such that $5x + y = 99$. The number of such distinct triangles whose area is a positive integer is:

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ courses are compulsory for every student?

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?