Practice Questions
Concept Explanation
When repetition is allowed, each position can be filled independently. When identical items exist, divide by factorials of repeat counts.
Key Formulas
- With repetition: nr arrangements of r objects from n types
- Identical items: n! / (p! q! r! …) for n objects with repeats
- Multiset formula removes overcounting from identical letters
Example
3-digit numbers using {1,2,3,4,5} with repetition: 53 = 125.
Common Trap
Use nr only when repetition is allowed; use n!/(p!q!) when items are identical.
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Q1 Easy
How many 3-digit numbers using digits 1–5 with repetition allowed?
Explanation5^3 = 125. -
Q2 Medium
How many 4-letter strings from {A,B,C} with repetition?
Explanation3^4 = 81. -
Q3 Hard
Arrangements of the letters of BANANA:
Explanation6!/(3!×2!) = 720/12 = 60. -
Q4 Easy
How many 2-digit numbers from digits 0–9 with repetition?
Explanation10^2 = 100. -
Q5 Medium
Arrangements of the word LEVEL:
Explanation5!/(2!×2!) = 120/4 = 30. -
Q6 Medium
How many ways to fill 4 boxes using 3 colours (repetition allowed)?
Explanation3^4 = 81. -
Q7 Hard
Arrangements of MISSISSIPPI:
Explanation11!/(4!×4!×2!) = 34650.
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Q8 Medium
How many 5-character passwords from 26 letters with repetition?
Explanation26^5 = 11881376. -
Q9 Easy
Arrangements of the word BOOK:
Explanation4!/(2!) = 24/2 = 12. -
Q10 Easy
How many 3-letter codes from {X,Y,Z} with repetition?
Explanation3^3 = 27. -
Q11 Hard
Arrangements of SUCCESS:
Explanation7!/(3!×2!) = 5040/12 = 420. -
Q12 Easy
How many 4-digit PINs using digits 0–9?
Explanation10^4 = 10000. -
Q13 Medium
Arrangements of PEPPER:
Explanation6!/(3!×2!) = 720/8 = 90. -
Q14 Medium
How many 3-digit numbers from {2,4,6,8} with repetition?
Explanation4^3 = 64.
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DS1 Easy
How many 3-digit numbers can be formed with repetition from digits 1–5?
Statement IDigits 1 through 5 may be reused.
Statement IIEach number has exactly 3 digits.
ExplanationStatement I alone: 5^3 = 125. -
DS2 Medium
How many distinct arrangements of the word BANANA exist?
Statement IThe word has 6 letters.
Statement IIIt contains 3 A's and 2 N's.
ExplanationNeed both: 6!/(3!×2!) = 60.
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DS3 Easy
How many 4-letter strings from 3 symbols with repetition?
Statement IThere are 3 symbols.
Statement IIRepetition is allowed.
ExplanationEach alone gives 3^4 = 81. -
DS4 Medium
How many arrangements of identical-colour balls exist?
Statement IThere are 5 balls: 2 red and 3 blue.
Statement IIAll balls are used in a row.
ExplanationStatement I alone: 5!/(2!×3!) = 10.