Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

How many different necklaces can be formed with $6$ white and $5$ red beads?

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?

The number of ways in which the letters of the word $TRIANGLE$ can be arranged such that no two vowels occur together is

Let $A_1, A_2, ......, A_{11}$ be players in a team with their $T$-shirts numbered $1, 2, ......, 11$. One hundred gold coins were won by the team. These coins are to be distributed among the players such that each player $A_i$ gets at least $i$ coins,plus an additional coin (i.e.,at least $i+1$ coins). Additionally,the captain (assume $A_1$) and vice-captain (assume $A_2$) must receive at least $5$ and $3$ coins more than their $T$-shirt numbers respectively. In how many different ways can these coins be distributed?