Practice Questions
Concept Explanation
Word arrangement problems count permutations of letters with or without restrictions (fixed letters, vowels together, etc.).
Key Formulas
- All distinct letters: n!
- With repeats: n! / (p! q! …)
- Vowels together: treat block as one unit, then arrange units
Example
Arrangements of TABLE (5 distinct letters) = 5! = 120.
Common Trap
Divide by factorials of identical letters; treat letter blocks as single units when together.
-
Q1 Easy
Arrangements of the word TABLE:
Explanation5 distinct letters: 5! = 120. -
Q2 Easy
Arrangements of the word BALL:
Explanation4!/(2!) = 24/2 = 12. -
Q3 Hard
Arrangements of MATHEMATICS:
Explanation11!/(2!×2!×2!×2!) = 4989600. -
Q4 Easy
Arrangements of CAT with C fixed at start:
ExplanationFix C; arrange A,T: 2! = 2. -
Q5 Easy
Arrangements of DOG with vowels together (none) — all arrangements:
Explanation3! = 6. -
Q6 Medium
Arrangements of LETTER:
Explanation6!/(3!×2!) = 720/4 = 180. -
Q7 Medium
Arrangements of APPLE with A at both ends:
ExplanationFix A at ends; arrange P,P,L in middle: 3!/2! = 3.
-
Q8 Medium
Arrangements of WORD with vowel O in a fixed vowel block (all valid arrangements):
ExplanationWith one vowel, all 4! = 24 arrangements satisfy the condition. -
Q9 Medium
Arrangements of BANANA:
Explanation6!/(3!×2!) = 60. -
Q10 Easy
Arrangements of TEAM with T at start:
ExplanationFix T; arrange E,A,M: 3! = 6. -
Q11 Easy
Arrangements of MISS:
Explanation3!/(2!) = 3. -
Q12 Medium
Arrangements of ABCDE with A and E at ends:
ExplanationA/E at ends: 2 ways. Middle 3: 3! = 6. Total = 12. -
Q13 Hard
Arrangements of COMMITTEE:
Explanation9!/(2!×2!×2!) = 907200. -
Q14 Medium
Arrangements of RADAR:
Explanation5!/(2!×2!) = 120/4 = 30.
-
DS1 Easy
How many arrangements of the word TABLE exist?
Statement IAll 5 letters are distinct.
Statement IINo letter position is fixed.
ExplanationStatement I alone: 5! = 120. -
DS2 Medium
How many arrangements of BANANA exist?
Statement IThe word has 6 letters.
Statement IIIt contains repeated letters.
ExplanationNeed both: 6!/(3!×2!) = 60.
-
DS3 Easy
How many arrangements with a fixed first letter?
Statement IThe word is CAT.
Statement IIThe first letter must be C.
ExplanationStatement II alone: fix C, arrange 2 letters = 2. -
DS4 Medium
How many arrangements with vowels together in WORD?
Statement IThe word has one vowel O.
Statement IIVowels must appear in consecutive positions.
ExplanationNeed both: WORD has 4 distinct letters; one vowel is always consecutive, so 4! = 24.