We will solve a challenging yet exciting puzzle today. It will test your mathematical and logical thinking skills to the fullest.
Moreover, you can try the challenge with your friends and have a fun event.
Here is the question:
A bag holds tiles with the letters A, E, I, O, and U. Which option of combinations is absent from the table that displays the possible outcomes for randomly choosing two letters from the bag without any replacement?
| AE | AI | AO | AU |
| EA | EI | EO | EU |
| IA | IE | IO | IU |
| OA | OE | OI | OU |
a) AA, EE, II, OO
b) UA, UE, UI, UO
c) UU, UA, UE, UI
d) IE, UO, UA, AI
Put on your thinking hats and give it a try. We will present the solution and explanation below for checking your answer.
Detailed Explanation and Answer
We have to select two letters in succession without putting the first one back. Then, we can determine the missing letter combinations when randomly choosing two letters out of the bag without replacement.
All Possible Two Letter Combinations
We can list all possible combinations and identify which ones are missing. Since we have five letters in the bag (A, E, I, O, U), all the possible combinations are:
- AE
- AI
- AO
- AU
- EI
- EO
- EU
- IO
- IU
- OU
Missing Combinations
Now, let us identify all the missing combinations. The list of letters missing from the table is as follows:
- AA
- EE
- II
- OO
- UU
These combinations are missing because you can’t select the same letter twice without replacement.
Therefore, the missing combination from the four options in our question is:
a) AA, EE, II, OO
This is the correct answer. Does your answer match with this?
Have Fun Solving Fun Challenges
We will have more challenges for you in the future. Please keep your eyes on our blog.
Last Updated on September 13, 2023 by Dipanjan
