People arrangements in groups/rows

A question is this type if and only if it involves arranging people into multiple groups, rows, or teams with specific composition requirements.

5 questions

CAIE S1 2009 June Q4
4 A choir consists of 13 sopranos, 12 altos, 6 tenors and 7 basses. A group consisting of 10 sopranos, 9 altos, 4 tenors and 4 basses is to be chosen from the choir.
  1. In how many different ways can the group be chosen?
  2. In how many ways can the 10 chosen sopranos be arranged in a line if the 6 tallest stand next to each other?
  3. The 4 tenors and 4 basses in the group stand in a single line with all the tenors next to each other and all the basses next to each other. How many possible arrangements are there if three of the tenors refuse to stand next to any of the basses?
CAIE S1 2013 June Q7
7 There are 10 spaniels, 14 retrievers and 6 poodles at a dog show. 7 dogs are selected to go through to the final.
  1. How many selections of 7 different dogs can be made if there must be at least 1 spaniel, at least 2 retrievers and at least 3 poodles? 2 spaniels, 2 retrievers and 3 poodles go through to the final. They are placed in a line.
  2. How many different arrangements of these 7 dogs are there if the spaniels stand together and the retrievers stand together?
  3. How many different arrangements of these 7 dogs are there if no poodle is next to another poodle?
CAIE S1 2015 June Q7
7 Rachel has 3 types of ornament. She has 6 different wooden animals, 4 different sea-shells and 3 different pottery ducks.
  1. She lets her daughter Cherry choose 5 ornaments to play with. Cherry chooses at least 1 of each type of ornament. How many different selections can Cherry make? Rachel displays 10 of the 13 ornaments in a row on her window-sill. Find the number of different arrangements that are possible if
  2. she has a duck at each end of the row and no ducks anywhere else,
  3. she has a duck at each end of the row and wooden animals and sea-shells are placed alternately in the positions in between.
CAIE S1 2016 March Q6
6 Hannah chooses 5 singers from 15 applicants to appear in a concert. She lists the 5 singers in the order in which they will perform.
  1. How many different lists can Hannah make? Of the 15 applicants, 10 are female and 5 are male.
  2. Find the number of lists in which the first performer is male, the second is female, the third is male, the fourth is female and the fifth is male. Hannah's friend Ami would like the group of 5 performers to include more males than females. The order in which they perform is no longer relevant.
  3. Find the number of different selections of 5 performers with more males than females.
  4. Two of the applicants are Mr and Mrs Blake. Find the number of different selections that include Mr and Mrs Blake and also fulfil Ami's requirement.
CAIE S1 2014 November Q6
6
  1. Seven fair dice each with faces marked 1,2,3,4,5,6 are thrown and placed in a line. Find the number of possible arrangements where the sum of the numbers at each end of the line add up to 4 .
  2. Find the number of ways in which 9 different computer games can be shared out between Wainah, Jingyi and Hebe so that each person receives an odd number of computer games.