Arranging identical items in a line

Arrange identical items of different types in a line or row, counting distinct arrangements (e.g., arranging identical packets of different products on a shelf, arranging identical colored items in sequence).

3 questions · Standard +0.3

5.01b Selection/arrangement: probability problems
Sort by: Default | Easiest first | Hardest first
CAIE S1 2017 March Q5
9 marks Standard +0.3
5
  1. A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number of cakes.
  2. Another plate holds 7 cup cakes, each with a different colour icing, and 4 brownies, each of a different size. Find the number of different ways these 11 cakes can be arranged in a row if no brownie is next to another brownie.
  3. A plate of biscuits holds 4 identical chocolate biscuits, 6 identical shortbread biscuits and 2 identical gingerbread biscuits. These biscuits are all placed in a row. Find how many different arrangements are possible if the chocolate biscuits are all kept together.
CAIE S1 2012 November Q7
12 marks Standard +0.3
7
  1. In a sweet shop 5 identical packets of toffees, 4 identical packets of fruit gums and 9 identical packets of chocolates are arranged in a line on a shelf. Find the number of different arrangements of the packets that are possible if the packets of chocolates are kept together.
  2. Jessica buys 8 different packets of biscuits. She then chooses 4 of these packets.
    1. How many different choices are possible if the order in which Jessica chooses the 4 packets is taken into account? The 8 packets include 1 packet of chocolate biscuits and 1 packet of custard creams.
    2. How many different choices are possible if the order in which Jessica chooses the 4 packets is taken into account and the packet of chocolate biscuits and the packet of custard creams are both chosen?
  3. 9 different fruit pies are to be divided between 3 people so that each person gets an odd number of pies. Find the number of ways this can be done.
Pre-U Pre-U 9794/3 2013 June Q5
10 marks Standard +0.3
5 A game is played with cards, each of which has a single digit printed on it. Eleanor has 7 cards with the digits \(1,1,2,3,4,5,6\) on them.
  1. How many different 7-digit numbers can be made by arranging Eleanor's cards?
  2. Eleanor is going to select 5 of the 7 cards and use them to form a 5 -digit number. How many different 5-digit numbers are possible?