CAIE S1 2014 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicPermutations & Arrangements
TypeArrangements with alternating patterns

6 Find the number of different ways in which all 8 letters of the word TANZANIA can be arranged so that
  1. all the letters A are together,
  2. the first letter is a consonant ( \(\mathrm { T } , \mathrm { N } , \mathrm { Z }\) ), the second letter is a vowel ( \(\mathrm { A } , \mathrm { I }\) ), the third letter is a consonant, the fourth letter is a vowel, and so on alternately. 4 of the 8 letters of the word TANZANIA are selected. How many possible selections contain
  3. exactly 1 N and 1 A ,
  4. exactly 1 N ?