Practice Questions
Concept Explanation
Factorial n! is the product of all positive integers from 1 to n. It forms the basis of permutations and combinations.
Key Formulas
- n! = n × (n − 1) × … × 2 × 1
- 0! = 1 (by definition)
- n! / (n − r)! = n × (n − 1) × … × (n − r + 1)
Example
5! = 5 × 4 × 3 × 2 × 1 = 120.
Common Trap
Do not treat 0! as 0. Remember 0! = 1.
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Q1 EasyWhat is the value of 5!?Explanation5! = 5 × 4 × 3 × 2 × 1 = 120. Hence the answer is 120.
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Q2 EasyWhat is the value of 1! + 2! + 3!?Explanation1! = 1, 2! = 2 and 3! = 6. Sum = 1 + 2 + 6 = 9. Hence the answer is 9.
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Q3 EasyWhat is the value of 0!?ExplanationBy standard mathematical definition used in permutations and combinations, 0! = 1. Hence the answer is 1.
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Q4 EasyWhat is the value of 6!?Explanation6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. Hence the answer is 720.
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Q5 EasyWhich of the following is equal to 720?Explanation5! = 120, 6! = 720, 7! = 5040 and 8! = 40320. Therefore 720 = 6!. Hence the answer is 6!.
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Q6 EasyEvaluate 3! × 2! / 2!.Explanation3! = 6 and 2! = 2, so (3! × 2!) / 2! = (6 × 2) / 2 = 6. Hence the answer is 6.
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Q7 MediumEvaluate 7! / 5!.ExplanationBy definition, n! = n × (n − 1) × … × 1, so 7! / 5! = (7 × 6 × 5!) / 5! = 7 × 6 = 42. Hence the answer is 42.
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Q8 MediumWhat is the value of 4! × 3!?ExplanationCompute 4! = 4 × 3 × 2 × 1 = 24 and 3! = 6. Then 4! × 3! = 24 × 6 = 144. Hence the answer is 144.
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Q9 MediumEvaluate 5! / 3!.Explanation5! / 3! = (5 × 4 × 3!) / 3! = 5 × 4 = 20. Hence the answer is 20.
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Q10 MediumEvaluate 8! / 6!.Explanation8! / 6! = (8 × 7 × 6!) / 6! = 8 × 7 = 56. Hence the answer is 56.
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Q11 MediumWhat is the value of 9! / 7!?Explanation9! / 7! = (9 × 8 × 7!) / 7! = 9 × 8 = 72. Hence the answer is 72.
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Q12 MediumEvaluate 10! / 8!.Explanation10! / 8! = (10 × 9 × 8!) / 8! = 10 × 9 = 90. Hence the answer is 90.
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Q13 HardEvaluate 12! / 10!.Explanation12! / 10! = (12 × 11 × 10!) / 10! = 12 × 11 = 132. Hence the answer is 132.
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Q14 HardWhat is the value of 11! / 9!?Explanation11! / 9! = (11 × 10 × 9!) / 9! = 11 × 10 = 110. Hence the answer is 110.
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DS1 Easy
What is the value of n!?
Statement IIt is given that n = 6.
Statement IIIt is given that n! = 720.
ExplanationFrom Statement I, n! = 6! = 720. From Statement II, the value is directly 720. Each statement alone is sufficient. Answer: D. -
DS2 Easy
For the value of 0! + 1! + 2!. What is that sum?
Statement IBy definition, 0! equals 1.
Statement IIIt is given that 1! = 1 and 2! = 2.
ExplanationStatement I alone does not give 1! and 2!. Statement II alone does not give 0!. Together, sum = 1 + 1 + 2 = 4. Both are needed. Answer: C.
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DS3 Medium
What is the value of 8! / 5!?
Statement IThe value of 8! is 40320.
Statement IIThe value of 5! is 120.
ExplanationStatement I alone lacks 5!. Statement II alone lacks 8!. Together, 8! / 5! = 40320 / 120 = 336. Both are needed. Answer: C. -
DS4 Medium
An HR analytics quiz asks: is n! divisible by 10?
Statement IIt is given that n = 5.
Statement IIIt is given that n = 6.
ExplanationIf n = 5, then 5! = 120, which is divisible by 10. If n = 6, then 6! = 720, which is also divisible by 10. Each statement alone answers the question. Answer: D.