The total number of permutations of the letters of the word "$BANANA$" is

$A$ 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?

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

For a scholarship,at most $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selecting at least one candidate for the scholarship is $63$,then the maximum number of candidates that can be selected for the scholarship is -

How many numbers lying between $10$ and $1000$ can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is allowed)?

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is