Question

Suppose you want to form words with 3 letters and all letters in the alphabet can be used except A and B (so, XYZ would be a word for example even though it does not make sense).

a) How many possibilities do you have if repetition is permitted and ordering is relevant, how many possibilities do you have if repetition is not permitted and ordering is relevant; how many possibilities do you have if repetition is not permitted and ordering is irrelevant? (3 points)

b) Where did you compute the number of permutations, where did you com- pute the number of combinations? (2 points)

c) Translate the three versions into the language of boxes and objects! (each separately)

Answer 1

We have to form words with three letters and all letters in the alphabet can be used except A and B.

Therefore there are total 24 letters we have to use to form a three letter words.

a. The number of possible way we can form three letter words, if repetition is allowed and ordering is relevant by: 24*24*24=13824

Since repetition is allowed for every single place we have 24 choices.

The number of possible ways we can form three letter words if repetition is not allowed and ordering is relevant by 24*23*22=12144

Repetition is not allowed there are 24 choices for first later 23 choices for second letter and 22 choices for 3rd letter.

the number of possible ways we can form three letter word if repetition is not allowed and ordering is irrelevant by:

Since ordering is irrelevant XYZ is same as XZY, YZX, YXZ, ZXY, ZYX.

b. Where ordering is important we used permutation.

Where ordering is irrelevant and repetition is not allowed we used combinations.

c. The origins can be translated into the language of boxes are:

i. Permutation of 24 boxes taken 3 at a time when repetition is allowed.

ii. Permutation of 24 boxes taken 3 at a time when repetition is not allowed.

iii. Combination of 24 boxes taken 3 at a time without repetition.

In case of objects:

I. Arrangements of three objects out of 24 objects with repetition.

II. Arrangements of three objects out of 24 objects without repetition.

III. Selection of three objects out of 24 objects.