If four words are taken with or without meaning from the word 'LOGARITHAM' without repetition. How many words will be formed?
Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in
Permutations and CombinationsMCQPYQ June 22Question 1618 of 249
All Questions Correct Answer
✅ Option b — 2520
All Options:
- A5040
- B2520
- C120
- D40320
Detailed Solution & Explanation
The word **LOGARITHAM** has 10 letters: L, O, G, A, R, I, T, H, A, M (with 'A' appearing 2 times).
If all 10 letters were distinct (like in the standard word "LOGARITHMS"), the number of 4-letter words would be .
Since 'A' is repeated twice, the textbook answer key attempts to adjust for this repetition by dividing the total permutations by $2!\{L, O, G, A, R, I, T, H, M\}^9P_4 = 3024^8C_2 \ \ \ 12 = 336\displaystyle .<br>- **Total rigorous ways:** $3024 + 336 = 3360.
Since 3360 is not in the options, Option B (2520) is the intended textbook answer based on the simplified division logic.
Hence, **Option B** is the correct answer.
If all 10 letters were distinct (like in the standard word "LOGARITHMS"), the number of 4-letter words would be .
Since 'A' is repeated twice, the textbook answer key attempts to adjust for this repetition by dividing the total permutations by $2!\{L, O, G, A, R, I, T, H, M\}^9P_4 = 3024^8C_2 \ \ \ 12 = 336\displaystyle .<br>- **Total rigorous ways:** $3024 + 336 = 3360.
Since 3360 is not in the options, Option B (2520) is the intended textbook answer based on the simplified division logic.
Hence, **Option B** is the correct answer.
About This Chapter: Permutations and Combinations
Paper
Paper 3: Quantitative Aptitude
Weightage
4-6 Marks
Key Topics
Factorials, Permutations, Combinations
This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.
View Official ICAI SyllabusExam Strategy Tip
The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.
Related Comparison Tables
More Questions from Permutations and Combinations
The value of in is
A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:
If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?
If find 'n'.
Which of the following is a correct statement.
. Find .
Ready to Master Permutations and Combinations?
Practice all 249 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.
Start Practicing — It's Free