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

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

There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit

Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are

How many numbers greater than $1000000$ can be formed by using the digits $1,2,0,2,4,2,4 ?$

Words of length $10$ are formed using the letters, $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated ; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$