$A$ coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

How many $3$-digit numbers can be formed from the digits $1, 2, 3, 4,$ and $5$ assuming that repetition of the digits is not allowed?

Eleven books consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?

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,$\frac{y}{9x} =$

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?