Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Determine the number of different arrangements of all 9 letters in the word AUSTRALIA for each of the following situations.
(a(i))[3]

All the vowels (A, I, U are vowels) are adjacent.

(a(ii))[3]

The letter T occupies the centre, and each end position is filled by one of the other consonants (R, S, L).

(b)[4]

Donna has 2 necklaces, 8 rings and 4 bracelets, all different. She selects 4 pieces of jewellery. How many different selections are possible if she chooses at least 1 necklace and at least 1 bracelet?

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct approach that groups the consonants and the vowels, for example $k\times5!$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI