Answer (Detailed Solution Below)

Option 2 : 5
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NDA 01/2025: English Subject Test
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Detailed Solution

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Formula used:

n! = n(n - 1)(n - 2)(n - 3).....3.2.1

Calculation:

Given that,

(n + 3)! = 56 [(n + 1)!]

⇒ (n + 3)(n + 2)(n + 1)! = 56[(n + 1)!]

⇒ (n + 3)(n + 2) = 56

⇒ n2 + 5n - 50 = 0

⇒ n2 + 10n - 5n - 50 = 0

⇒ (n + 10)(n - 5) = 0

⇒ n = 5, - 10

Hence, n = 5 is the required value.

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