The number of ways of getting a sum of $16$ when throwing a die four times is:

The number of four-lettered words that can be formed from the letters of the word $MAYANK$ such that both $A$'s are included but never together,is equal to:

How many six-digit numbers are there in which no digit is repeated,even digits appear at even places,odd digits appear at odd places,and the number is divisible by $4$?

In an examination,there are $3$ multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is:

Three and four digit numbers are formed from the digits $1, 3, 5, 6, 8$. If $e_1$ is the number of three-digit even numbers with no digit repeated and $e_2$ is the number of four-digit even numbers with no digit repeated. Also,$O_1$ represents the number of three-digit odd numbers in which no digit is repeated and $O_2$ represents the number of four-digit odd numbers in which no digit is repeated. Then:

$A$ man $X$ has $7$ friends,$4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends,$3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. The total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men,such that $3$ friends of each of $X$ and $Y$ are invited,is: