SOLUTION: 3. Construct a table listing all possible samples of size 7 Combination: 87, 92, 93, 93, 94, 94, 95, 96, 97 Must be 36 samples

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Question 1194633: 3. Construct a table listing all possible samples of size 7
Combination: 87, 92, 93, 93, 94, 94, 95, 96, 97

Must be 36 samples
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


That's a job that you can do yourself; we aren't going to do all the tedious work for you....

You are choosing 7 of the 9 elements in the set; the number of combinations is C(9,7) = 36.

The number C(9,7) is the same as the number C(9,2) -- each group of 7 of the 9 that you choose corresponds to a group of 2 that you do NOT choose.

Use that idea to make it easier to make your list. Make a list of each group of 2 you can NOT choose and find the corresponding group of 7 for your list. For example....
   not chosen         chosen
  (group of 2)     (group of 7)
  ----------------------------------------
    87, 92     93, 93, 94, 94, 95, 96, 97
    93, 93     87, 92, 94, 94, 95, 96, 97
    94, 97     87, 92, 93, 93, 94, 95, 96
    ...        ...
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

As the other tutor mentioned, you can form subsets of size 7 by picking subsets of size 2.
Whatever 2 items you pick, they will be ignored so you can focus on the other 7 items.

Because this value 2 shows up, it may be handy to form a two-way table. In this case, we'll have a 9 row and 9 column two-way table like this.
879293939494959697
87
92
93
93
94
94
95
96
97


Write X's along the main diagonal.
This is because we cannot select the same item twice when forming a 2 element subset.
879293939494959697
87X
92X
93X
93X
94X
94X
95X
96X
97X


We'll also write X's in every entry below the diagonal.
Why? Notice that stuff below the diagonal mirrors the stuff above the diagonal.
Example: look at row 2, column 1 and you'll see we're dealing with the same values as row 1, column 2. Both of those values being 87 and 92 in either order.
879293939494959697
87X
92XX
93XXX
93XXXX
94XXXXX
94XXXXXX
95XXXXXXX
96XXXXXXXX
97XXXXXXXXX


The empty cells that haven't been crossed out are then filled with the 7 element subsets
For example, in row 1, column 2 we'll have the subset {93, 93, 94, 94, 95, 96, 97} which is everything except the 87 & 92
879293939494959697
87X{93, 93, 94, 94, 95, 96, 97}
92XX
93XXX
93XXXX
94XXXXX
94XXXXXX
95XXXXXXX
96XXXXXXXX
97XXXXXXXXX



I'll let you fill out the rest.

Edit: I realize that there are duplicate entries (93 and 94). I'm not sure if your teacher made a typo or not. I'll keep my answer as is, since it may be useful for similar types of problems of this nature.
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