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?

Find the number of arrangements of the letters of the word '$ALGEBRA$' without altering the relative position of the vowels and the consonants.

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

In a plane there are $37$ straight lines of which $13$ pass through the point $A$ and $11$ pass through the point $B$. Besides,no three lines pass through one point,no line passes through both points $A$ and $B$,and no two lines are parallel. Then the number of intersection points the lines have is equal to

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

In how many ways can $10$ balls be divided between two boys,if one receives two balls and the other receives eight balls?