How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Five racquets need to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?

There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?

Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike?

A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?

Can you calculate in how many ways can 7 tennis players can be seated in a circular order?

Please calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?