(a) Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases.
(i) All the vowels (A, I, U are vowels) are together.
(ii) The letter T is in the central position and each end position is occupied by one of the other consonants (R, S, L).
(b) Donna has 2 necklaces, 8 rings and 4 bracelets, all different. She chooses 4 pieces of jewellery. How many possible selections can she make if she chooses at least 1 necklace and at least 1 bracelet?

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 10 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics May/June 2018 examination, Paper 6 Variant 2 (9709_s18_qp_62.pdf).

Question

(a) Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases.
(i) All the vowels (A, I, U are vowels) are together.
(ii) The letter T is in the central position and each end position is occupied by one of the other consonants (R, S, L).
(b) Donna has 2 necklaces, 8 rings and 4 bracelets, all different. She chooses 4 pieces of jewellery. How many possible selections can she make if she chooses at least 1 necklace and at least 1 bracelet?

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