In a club with 21 members, how many ways can a slate of 3 officers consisting of president, vice- president, and secretary be chosen?___Find the number of distinguishable permutations of the letters in the word "decreed".___A child has a set of differently shaped plastic objects. There are 5 pyramids, 3 cubes, and 6 spheres. How many arrangements are possible if objects of the same shape must be grouped together and each object is a different color?___In how many distinguishable ways can the objects be arranged in a row if objects of the same shape are also the same color, but need not be grouped together?___In how many ways can you select 3 objects, one of each shape, if the order in which the objects are selected does not matter and each object is a different color?___A committee of 12 members must form a sub-committee to present a paper. How many ways can a 5 member sub-committee be formed if none are to be given special tasks?___How many ways can a 5 member sub-committee be formed if one member is to be the chair and another the recorder?___How many ways can a 5 member sub-committee be formed if the chair of the larger committee must be a member of the subcommittee?___