A bag holds tiles with the letters a e i o n u which list of letter combinations is missing from the table that shows the possible outcomes for randomly choosing two letters out of the bag without replacement
There are a total of 6 letters in the bag, so the number of possible outcomes for choosing two letters without replacement is:
6 choose 2 = 15
To create a table of all possible outcomes, we can list each letter combination once, in alphabetical order:
- ae
- ai
- ao
- an
- au
- ei
- eo
- en
- eu
- io
- in
- iu
- on
- ou
- nu
Therefore, there are no missing letter combinations from the table.
To determine the missing letter combinations when randomly choosing two letters without replacement from the bag, we can use the concept of combinations.
The formula to calculate the number of combinations is:
nCr = n! / r!(n-r)!
Where n is the total number of items in the set (in this case, the number of tiles in the bag), and r is the number of items chosen at a time (in this case, 2 letters).
Let's calculate the combinations:
1. Calculate the total number of letters in the bag, n:
In this case, there are 6 letters in the bag: a, e, i, o, n, u. So, n = 6.
2. Calculate the combinations for choosing 2 letters, nCr:
nCr = 6! / 2!(6-2)!
= 6! / 2!4!
= (6 * 5 * 4 * 3 * 2 * 1) / ((2 * 1) * (4 * 3 * 2 * 1))
= (720) / (4 * 6)
= 720 / 24
= 30
Therefore, there are 30 different letter combinations when choosing 2 letters without replacement from the bag.
Now, to determine the missing letter combinations, we need to list all the possible combinations and identify the ones that are missing.
Here are all the possible letter combinations:
ae, ai, ao, an, au
ei, eo, en, eu
io, in, iu
on, ou
nu
From this list, we can see that the following combinations are missing:
ae, au
ei, eu
io, iu
on, ou
So, the missing letter combinations from the table are:
ae, au
ei, eu
io, iu
on, ou