Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Determine how many distinct arrangements of all $8$ letters in the word TANZANIA are possible so that
(i)[2]

the $A$ letters are all adjacent,

(ii)[3]

the arrangement starts with a consonant ($T, N, Z$), the second position is a vowel ($A, I$), the third is a consonant, the fourth is a vowel, and the pattern continues alternately.

(iii)[2]

$4$ of the $8$ letters in TANZANIA are chosen. How many different selections include exactly $1$ $N$ and $1$ $A$?

(iv)[3]

$4$ of the $8$ letters in TANZANIA are chosen. How many different selections include exactly $1$ $N$?

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Noting $6!$

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