Multiple separation conditions combined

Questions with multiple simultaneous separation requirements (e.g., some items together AND other items not together, or fixed ends with separation constraints).

2 questions · Standard +0.3

5.01a Permutations and combinations: evaluate probabilities
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CAIE S1 2020 March Q4
6 marks Standard +0.3
4 Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He arranges the 11 candles in a line.
  1. Find the number of different arrangements of the 11 candles if there is a red candle at each end.
  2. Find the number of different arrangements of the 11 candles if all the blue candles are together and the red candles are not together.
CAIE S1 2023 March Q7
12 marks Standard +0.3
  1. Find the number of different arrangements of the 9 letters in the word DELIVERED in which the three Es are together and the two Ds are not next to each other. [4]
  2. Find the probability that a randomly chosen arrangement of the 9 letters in the word DELIVERED has exactly 4 letters between the two Ds. [5]
Five letters are selected from the 9 letters in the word DELIVERED.
  1. Find the number of different selections if the 5 letters include at least one D and at least one E. [3]