Q.Find n, if: [equation involving n, 8!, 6!, 3! — a stacked-fraction expression whose exact layout could not be confidently reconstructed from the extracted text]
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Start your 14-day free trial to unlock the full solution →Concept understanding — Factorial Notation
For a natural number , the factorial of , written , is the product of all natural numbers from 1 up to : . It can equally be read in the reverse (and often more useful) order, , which is what makes properties like so natural: the factorial of a number is that number times the factorial of the number just below it. By convention, is defined to equal (even though 0 is not itself a natural number), which keeps formulas like and consistent without needing a special-case exception. Factorial notation grows extremely fast ( is already over 3.6 million), so most factorial computations in practice are done by CANCELLING a shared tail between a numerator and a denominator (writing the larger factorial as extra factors times the smaller one) rather than by expanding both fully — this is the technique behind simplifying expressions like …
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