Counting methods and probability theories 1. A scrambled word game challenges th

Question

Counting methods and probability theories

1. A scrambled word game challenges the user to create three-letter words (nonsense words included) from five different letters. If a letter cannot be used in a word more than once, how many potential words can be created?

2. How many license plates containing seven characters can be created from letters and numbers if the first two characters must be uppercase letters and the last five characters must be digits from 0 to 9? Repetition of numbers is allowed. Repetition of letters is not allowed.

3. How many ways can you rank your top three movies from the 38 movies on your laptop?

Please show work.

Explanation / Answer

Solution:

1. Since we are having 5 different letters and we have to chose 3 letters word without any repeatition

therefore

first can be chosen = 5 ways

second can be chosen = 4 ways

and last can be chosen = 3 ways

potential words can be created = 5 x 4 x 3 = 60 ways

(2)

first letter can be selected for 7 th place = 26 ways

and second letter can be selected for 6 th place = 25 ways

and selection number for reamining 5 places = 10 x 9 x 8 x 7 x6

license plates containing seven characters can be created = 25 x 26 x 10 x9x8x7x6

= 19656000

(3)

Let first movie can be chosen form 38 movies = 38 ways

and second movie = 37 ways

and third movie = 36 ways

therefore

number of ways you can rank your top three movies from the 38 movies = 38 x 37 x36

= 50616 ways

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