Use a table to llustratethe permutation of the following set of object
A. A strawberry a chocolate and a sugar glazed donut arranged in a row
B.A cup a glass and a might arranged in a row
C. The five vowels of the alphabet arranged in a row
D.Ways by which you can dress up if you have 3 skirts 4 shirts and 3 pairs of sandals?
E. The order by which joy Susan and Janice can enter a room
*mug not might
Sure! Let's go through each question one by one and use a table to illustrate the permutations:
A. A strawberry, a chocolate, and a sugar-glazed donut arranged in a row:
To find the number of permutations, we can use the formula n!, where n is the number of objects. In this case, we have 3 objects, so the number of permutations is 3!.
Using a table, we can list all the possible arrangements:
| | 1st Object | 2nd Object | 3rd Object |
|-------|------------|------------|------------|
| Arr 1 | Strawberry | Chocolate | Donut |
| Arr 2 | Strawberry | Donut | Chocolate |
| Arr 3 | Chocolate | Strawberry | Donut |
| Arr 4 | Chocolate | Donut | Strawberry |
| Arr 5 | Donut | Strawberry | Chocolate |
| Arr 6 | Donut | Chocolate | Strawberry |
B. A cup, a glass, and a mug arranged in a row:
Using the same formula, we have 3 objects, so the number of permutations is 3!.
| | 1st Object | 2nd Object | 3rd Object |
|-------|------------|------------|------------|
| Arr 1 | Cup | Glass | Mug |
| Arr 2 | Cup | Mug | Glass |
| Arr 3 | Glass | Cup | Mug |
| Arr 4 | Glass | Mug | Cup |
| Arr 5 | Mug | Cup | Glass |
| Arr 6 | Mug | Glass | Cup |
C. The five vowels of the alphabet arranged in a row:
In this case, we have 5 objects, so the number of permutations is 5!.
| | 1st Object | 2nd Object | 3rd Object | 4th Object | 5th Object |
|-------|------------|------------|------------|------------|------------|
| Arr 1 | A | E | I | O | U |
| Arr 2 | A | E | I | U | O |
| Arr 3 | A | E | O | I | U |
| Arr 4 | A | E | O | U | I |
| Arr 5 | A | E | U | I | O |
| ... | ... | ... | ... | ... | ... |
D. Ways to dress up with 3 skirts, 4 shirts, and 3 pairs of sandals:
Since we have different objects (skirts, shirts, sandals), we can use the formula for permutations with repetition. The formula is n! / (n1! * n2! * ... * nk!), where n is the total number of objects, and ni represents the number of each type of object.
In this case, we have 10 objects in total (3 skirts, 4 shirts, and 3 pairs of sandals), so the number of ways to dress up is 10! / (3! * 4! * 3!). This would require more time to list all the arrangements in a table.
E. The order by which Joy, Susan, and Janice can enter a room:
In this case, we have 3 people, so the number of permutations is 3!.
| | 1st Person | 2nd Person | 3rd Person |
|-------|------------|------------|------------|
| Arr 1 | Joy | Susan | Janice |
| Arr 2 | Joy | Janice | Susan |
| Arr 3 | Susan | Joy | Janice |
| Arr 4 | Susan | Janice | Joy |
| Arr 5 | Janice | Joy | Susan |
| Arr 6 | Janice | Susan | Joy |
I hope this helps you understand how to use a table to illustrate permutations!