Basic arrangements with repeated letters

Questions asking for the number of arrangements of letters from a word containing repeated letters, with no additional constraints beyond arranging all or some of the letters.

6 questions · Moderate -0.6

5.01a Permutations and combinations: evaluate probabilities
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CAIE S1 2018 November Q1
5 marks Moderate -0.8
1
  1. How many different arrangements are there of the 11 letters in the word MISSISSIPPI?
  2. Two letters are chosen at random from the 11 letters in the word MISSISSIPPI. Find the probability that these two letters are the same.
OCR FD1 AS 2018 March Q1
10 marks Standard +0.3
1
  1. (a) Show that the number of arrangements of 25 distinct objects is an integer multiple of \(5 ^ { 6 }\).
    (b) Explain how this shows that the number of arrangements of 25 distinct objects is a whole number of millions.
  2. (a) Calculate the values of
Pre-U Pre-U 9794/3 2017 June Q4
9 marks Moderate -0.3
4 The letters of the word 'STATISTICS' are to be rearranged.
  1. How many distinct arrangements are there?
  2. How many of the arrangements start and end with the letter S ?
  3. What is the probability that, in a randomly chosen arrangement, the S's are all together?
CAIE S1 2002 June Q5
8 marks Moderate -0.3
The digits of the number 1223678 can be rearranged to give many different 7-digit numbers. Find how many different 7-digit numbers can be made if
  1. there are no restrictions on the order of the digits, [2]
  2. the digits 1, 3, 7 (in any order) are next to each other, [3]
  3. these 7-digit numbers are even. [3]
OCR S1 2010 January Q8
7 marks Moderate -0.8
The five letters of the word NEVER are arranged in random order in a straight line.
  1. How many different orders of the letters are possible? [2]
  2. In how many of the possible orders are the two Es next to each other? [2]
  3. Find the probability that the first two letters in the order include exactly one letter E. [3]
Edexcel S2 Q1
6 marks Easy -1.8
  1. Explain briefly what you understand by the terms
    1. population,
    2. sample.
    [2 marks]
  2. Giving a reason for each of your answers, state whether you would use a census or a sample survey to investigate
    1. the dietary requirements of people attending a 4-day residential course,
    2. the lifetime of a particular type of battery.
    [4 marks]