Data Management Grade 12

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How many different five-letter words can be formed using the letters of the word STEVIN,
a) if only one vowel is to be used?
b) if both vowels are to be used and E is to precede I?
c) if both vowels must be used, they must be adjacent, and E is to precede I?
d) if either one vowel is to be used or E is to precede I?

  • Data Management Grade 12 -

    You must be familiar with the usual conventions of permutations, P(i,j), the number of ways of ordering i items out of j distinct items, where
    For example, how many 2 lettered words can be made of the letters a,b and c:

    You would be making 5 lettered words out of the 5 letters STEVN or STVIN.
    The number of words:

    You'd be making words out of
    for a total of
    4P(5,5) words.
    However, half of these words have the vowels in wrong order, so the answer should be 2P(5,5).

    Treat EI as one letter X, and choose 3 remaining letters to give
    So you have 4P(4,4) words.

    The two cases are mutually exclusive, so we just have to add cases a) and c).

    Check my work.

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