Anagram method for permutations and combinations.

[alok.sarsidharan]

Hi,

I'm not able to figure out when to use the number format (eg: 1234NNN) and when to use the yes/no (eg: YYYYNNN) format.

For example, consider the 2 problems provided below :

1> The principal of a high school needs to schedule observations of 6 teachers. She plans to visit one teacher each day for a week, so she will only have time to see 5 of the teachers. How many different observation schedules can she create?

2> A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If Lizzie wants to write a report that includes two or three of the birds, how many different reports can she write?


In the solution set, the number format is used for the 1st problem and yes/no format is used for the 2nd problem.

Can you please let me know how to decide which format to construct the anagram with? Since many of word problems use quite similar words, it becomes hard to segregate them.

[alok.sarsidharan]

Sorry, I didn't adhere to the posting rules.

The problems can be found in Chapter 4, page 61 (Combinatorics problem set : Q 9 & 10). I've posted two problems because a comparison was needed.

I'll first provide the solution to these problems(as given in the solution set of the book) and then pose my question :

Solution for 1> 720.
Following anagram was used :
A B C D E F
1 2 3 4 5 N
6! = 6*5*4*3*2*1 = 720.

Solution for 2>
First figure out the number of 2 bird reports as anagrams of the "word" YYNNNN
A B C D E F
Y Y N N N N
6! / 4!2! = 15
Then consider the number of 3 bird reports as the anagram of the "word" YYYNNN
6! / 3!3! = 20
All in all, there are 15 + 20 = 35 possible bird combinations.

My question :

Why can't we use the anagram YYYYYN for the 1st problem, and the anagrams "12NNNN" AND "123NNN" for the second problem?

[mikhsor]

Because the first problem is a permutation problem while the second is a combination problem. The order of visiting teachers is important to us because it will create differnet schedules, but which bird was chosen first, second and third is not important (it will not affect the report)

[Ben Ku]

Mikhsor stated it well:

Because the first problem is a permutation problem while the second is a combination problem. The order of visiting teachers is important to us because it will create differnet schedules, but which bird was chosen first, second and third is not important (it will not affect the report)

In the first problem, the numbers 1, 2, 3, 4, and 5 represent the order in which the teachers will be seen, or the day the teacher will be observed. For example, an order 1, 2, 3, 4, 5 is different from 1, 2, 3, 5, 4, since the last two teachers will be observed in a different order.

In the second problem, it doesn't matter if I pick birds A and B or birds B and A. Either way, the same birds are picked. I am only concerned about which birds are picked, and not the order in which they are picked.

Let me know if this explanation makes sense.