Forth Edition Word Translations, Combinometrics Pg 76 Q15

[saurabhbanerjeeiimk]

The question reads as "Gordon buys 5 dolls for his 5 nieces."

Why is 4!/2!= 12 being explained as the ways in which the youngest niece gets the GI doll. The calculation is based on the dolls OTHER than the GI doll.

[tim]

Exactly. If we want to calculate the number of ways to give the GI doll to the youngest niece, we give her the GI doll first and then calculate all the ways to give out the other dolls as well. Every one of these possibilities is different, but they all give the GI doll to the youngest niece..

[saurabhbanerjeeiimk]

Not clear yet :(

Q1. As per the answer, AFTER the GI doll is given to niece E, the combination for the 4 remaining dolls is calculated for the OTHER 4 nieces, i.e neice E is excluded from the 4 nieces. Which would imply that the 12 ways are for the 4 nieces.

Q2. Is this question based on the "Glue method"

If your answer to Q2 is Yes, then kindly explain the calculation related to the 4 remaining dolls (by correlating it to the Glue method)

Thanks a ton an advance!

[tim]

EXACTLY! There are 12 ways we can give the dolls out to the other 4 neices. You’re right; it sounds like you agree with me 100%. Unfortunately that means I’m not seeing where your question lies. This problem does not need to use the glue method, to answer your second question..

[pranabiitkgp]

Hi ,
I dont understand the slot method very well , but easy with permutation .
So can this be explained as bellow -
Is it a permutation of picking 5 out of 5 where 2 are same - 5P2/!2 ?
If this is correct so can it be like if there were 3 sisters instead of 5 , with all other condition intact ,the solution would have been -

Total # of ways to distribute SSEGT among 3 sisters (without restriction) is 5P3/!2 = 15;
The # of ways when the youngest niece gets G is: 4P2/!2 = 6 (give G to youngest and then distribute SSET among 2 sisters).

So, # of ways when youngest niece doesn't get G is:15-6 = 9 .

Please explain for better understanding . Thanks.

[pranabiitkgp]

a typo correction to my previous post -
Is it a permutation of picking 5 out of 5 where 2 are same - 5P5/!2

[jnelson0612]

a typo correction to my previous post -
Is it a permutation of picking 5 out of 5 where 2 are same - 5P5/!2

Correct! So your calculation is:

5!
2!1!1!1!

[adm45]

Why does the anagram have SSETG and SSET when all over previous any grams have usually have Yes NO or IN OUT?

Why is the glue method not applicable here? What is the trap that is making me think this and how can I avoid that?

Please explain what "pranabiitkgp" wrote; I don't understand the way she explains permutations, the symbols confuse me. Is there an exact page where these symbols are explained?

[jlucero]

Why does the anagram have SSETG and SSET when all over previous any grams have usually have Yes NO or IN OUT?

Why is the glue method not applicable here? What is the trap that is making me think this and how can I avoid that?

Please explain what "pranabiitkgp" wrote; I don't understand the way she explains permutations, the symbols confuse me. Is there an exact page where these symbols are explained?

pranabiitkgp is referencing a common way of selecting permutations- 5 pick 2, or 5 choose 2: If I have 5 things, I choose 2 of those things(5!/2!3!). Unfortunately, if I under him/her correctly (and it's very possible I don't), I don't think this works here because of your first question. We're not selecting 2 things and leaving 3 things behind. We're reordering five things, one which is a duplicate.

There's a few different ways you could do this problem, the glue method is one of them. You could find the number of arrangements when the youngest niece gets each of the four other types of dolls OR, you could glue the GI doll to the youngest niece and eliminate those possibilities from the total number of arrangements: 5!/2!1!1!1! - 4!/2!/1!/1! = 60 - 12 = 48