Question 1: Forming Words with Vowels

Question:
How many words (with or without meaning) can be formed using vowels? (Repetition allowed and not allowed)

• Vowels are: A, E, I, O, U → 5 vowels.

Answer:

• If repetition is allowed:
  Each position can have any vowel.
  So,

  5×5×5=5³=125 words

• If repetition is not allowed:
  Each position must have a different vowel.
  So,

  5×4×3=60 words

Explanation (Simple Language):

• Since all letters are used together, it’s a case of multiplication.

• With repetition → Same letter can appear again.

• Without repetition → No letter can be repeated; choices decrease.

Question 2: Posting Letters into Letterboxes

Question:
There are 4 letters and 5 letterboxes. In how many ways can the letters be posted?

Answer:

• Repetition is allowed — because a letterbox can receive multiple letters.
  (No rule that one box can hold only one letter.)

• So,

  5×5×5×5=5⁴ =625 ways

Short Approach Explanation:

• Letters are moving (not letterboxes).

• Make blanks for moving items → (Letter1, Letter2, Letter3, Letter4).

• Fill each blank with number of options (letterboxes = 5).

⚡ Note:
Answer is not 4⁵ because letterboxes cannot move toward the letters — that would be weird!

Question 3: Wearing Rings on Fingers

Question:
There are 3 rings and 4 fingers. In how many ways can the rings be worn?

Answer:

• No restriction (repetition allowed):
  Rings are moving to fingers.

  So,

  4×4×4=4³ =64 ways

• If repetition is not allowed (one finger holds only one ring):

  4×3×2=24 ways

Short Approach Explanation:

• Rings are movable → make blanks for rings.

• Fill each blank with number of fingers (4 options initially).

🚫 Wrong Approach:
If you mistakenly do 3⁴, it means fingers are moving to rings — not natural during a wedding ceremony (and sounds like a forced marriage 😅).

Question 4: Seating Persons on Chairs (More Chairs)

Question:
There are 5 persons and 8 chairs. How many seating arrangements are possible?

Answer:

• 8×7×6×5×4=6720 ways

Question 5: Seating Persons on Chairs (More Persons)

Question:
There are 8 persons and 5 chairs. How many seating arrangements are possible?

Answer:

This question is senseless in basic counting because you can’t seat 8 persons on 5 chairs without extra conditions like:

• Sitting on laps (which is not usual in standard problems 😅)

• Or standing/switching chairs (not considered here)

Thus, invalid without additional context.

Question 6: Password Formation

Question:
How many 3-letter passwords can be formed using 6 different alphabets if repetition is allowed?

Answer:
Each position has 6 choices.

6×6×6=6³=216 passwords

Question 7: Team Selection

Question:
A captain wants to select either a bowler (6 choices) or a batsman (5 choices) for a match. How many ways can he select?

Answer:
Feeling of either/or → Addition principle.

6+5=11 ways

Conclusion

Practicing these basic counting problems builds a strong foundation for more advanced topics like permutations, combinations, and probability.
Always remember:

• Multiplication → Feeling of “and”, “all”, “together”.

• Addition → Feeling of “or”, “either”, “only one”.

Next Up: We’ll explore permutations in detail with real-world examples!