The number of different signals which can be given from $7$ different coloured sheets,taking one or more at a time is

Consider $4$ boxes,where each box contains $3$ red balls and $2$ blue balls. Assume that all $20$ balls are distinct. In how many different ways can $10$ balls be chosen from these $4$ boxes so that from each box at least one red ball and one blue ball are chosen?

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is

The sum of the four-digit even numbers that can be formed with the digits $0, 3, 5, 4$ without repetition is:

All possible words (with or without meaning) are formed by taking at least $2$ letters (all different) from the letters of the word '$CURVE$'. If a word is chosen at random from all the words thus formed,then the probability of getting a $3$-letter word is