How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

The total number of ways of selecting six coins out of $20$ one-rupee coins,$10$ fifty-paise coins,and $7$ twenty-five-paise coins is:

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals