50+ factorials worksheets for 10th Year on Quizizz | Free & Printable - Free Printable

Let’s solve each problem step by step.

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Problem 1: Simplify 12! / 9!

We know that:
12! = 12 × 11 × 10 × 9!
So,

12! / 9! = (12 × 11 × 10 × 9!) / 9! = 12 × 11 × 10

Now calculate:

12 × 11 = 132
132 × 10 = 1320

✔ Final Answer for #1: 1320

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Problem 2: Simplify n! / (n - 2)!

Recall:
n! = n × (n-1) × (n-2)!
So,

n! / (n - 2)! = [n × (n-1) × (n-2)!] / (n-2)! = n × (n-1)

That matches option C

✔ Final Answer for #2: C

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Problem 3: Simplify n! / (n - 3)!

Similarly:
n! = n × (n-1) × (n-2) × (n-3)!
So,

n! / (n - 3)! = n × (n-1) × (n-2)

That matches option A

✔ Final Answer for #3: A

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Problem 4: Simplify 7! / [5(6 - 3)!]

First, simplify inside the parentheses:

6 - 3 = 3 → so denominator is 5 × 3!

3! = 6 → so denominator = 5 × 6 = 30

Numerator: 7! = 5040

So, 5040 / 30 = ?

Divide: 5040 ÷ 30 = 168

✔ Final Answer for #4: 168

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Problem 5: Simplify [12 × (10 - 6)!] / [3! × 2!]

Step 1: 10 - 6 = 4 → so numerator has 12 × 4!

4! = 24 → 12 × 24 = 288

Denominator: 3! = 6, 2! = 2 → 6 × 2 = 12

Now divide: 288 / 12 = 24

✔ Final Answer for #5: 24

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Problem 6: Evaluate to nearest whole number: 9! / (3! + 6!)

First, compute factorials:

9! = 362880
3! = 6
6! = 720
So denominator = 6 + 720 = 726

Now divide: 362880 ÷ 726

Let’s do this division carefully:

726 × 500 = 363000 → too big (since 363000 > 362880)

Try 726 × 499 = ?

Better to just divide directly:

362880 ÷ 726 ≈ ?

Use calculator-style steps:

726 × 499 = 726 × (500 - 1) = 363000 - 726 = 362274

362880 - 362274 = 606

So 499 + (606 / 726) ≈ 499 + 0.835 ≈ 499.835

Nearest whole number = 500

✔ Final Answer for #6: 500

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Final Answers:

1. 1320
2. C
3. A
4. 168
5. 24
6. 500