Question

4. The Hawaiian alphabet has twelve letters: five vowels (a, e, i, o, and u) and seven consonants (h, k, l, m, n, p, and w). For the purpose of this exercise we will define an n–letter “word” as an ordered collection of n of these twelve letters with repeats allowed. Obviously, most such “words” will be nonsense words.

  e) What is the probability a randomly selected four–letter “word” contains exactly one consonant?

Answer 1

To make a 4 letter word out of the available 12 alphabets, for every letter we have 12 choices. Therefore, total number of possible ways = 12×12×12×12 = 124 = 20736.

Now, to make a 4 letter word with exactly one consonant, let us first choose the letters to be placed in the 4 letter word.

For the consonant, we have 7 choices i.e. the consonant can be chosen in 7 ways.

Now, the remaining 3 letters are vowels, and for selecting each vowel we will have 5 choices.