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Question

Which of the following has(have) value(s) equal to the value 2! ?

A
5!3!
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B
(53)!
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C
2
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D
21
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Solution

The correct option is C 2
Let's first find the value of 2!, 2!=2×1=2

Now, let's simplify and find the values of all the given options one-by-one:

5!3!

5!3!=5×4×3×2×13×2×1

Taking out the common factors 3×2×1
5!3!=(5×41)×(3×2×1)

5!3!=(201)×6

5!3!=19×6

5!3!=114

As we can see that,
21142!5!3!

Therefore, the value of 5!3! is not equal to the value of 2!
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(53)!

(53)!=(2)!=2×1=2

As we can see that,
2=2
2!=(53)!

Therefore, the value of (53)! is equal to the value of 2!
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2
By definition only, 2! is equal to 2.
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21
The value of 2! is 2, hence, it can not be equal to 21.

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