Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

The total number of seven-digit numbers whose sum of digits is even is

All the letters of the word $TABLE$ are permuted and the strings of letters (may or may not have meaning) thus formed are arranged in dictionary order. Then the rank of the word $TABLE$ counted from the rank of the word $BLATE$ 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:

Number of all possible words (with or without meaning) that can be formed using all the letters of the word $CABINET$ in which neither the word $CAB$ nor the word $NET$ appear is

$A$ question paper has $3$ parts and each part contains $4$ questions. The number of different ways in which a candidate can answer $8$ questions choosing at least two from each part is