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For a positive integer n, the number n! is defined to be

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For a positive integer n, the number n! is defined to be [#permalink] New post   21 Dec 2018, 08:37
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For a positive integer n, the number n! is defined to be n(n - 1)(n - 2) ... (1). For example, 4! = 4(3)(2)(1). What is the value of 5! - 3!?

(A) 120
(B) 114
(C) 20
(D) 15
(E) 2
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Re: For a positive integer n, the number n! is defined to be [#permalink] New post   21 Dec 2018, 09:32
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HKD1710 wrote:
For a positive integer n, the number n! is defined to be n(n - 1)(n - 2) ... (1). For example, 4! = 4(3)(2)(1). What is the value of 5! - 3!?

(A) 120
(B) 114
(C) 20
(D) 15
(E) 2

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\(5! - 3!\)

= \(5*4*3! - 3!\)

= \(3!( 5*4 - 1)\)

= \(3*2 ( 20 - 1 )\)

= \(6*19\)

= \(114\), Answer must be (B)
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Re: For a positive integer n, the number n! is defined to be [#permalink] New post   21 Dec 2018, 10:33
HKD1710 wrote:
For a positive integer n, the number n! is defined to be n(n - 1)(n - 2) ... (1). For example, 4! = 4(3)(2)(1). What is the value of 5! - 3!?

(A) 120
(B) 114
(C) 20
(D) 15
(E) 2

Project PS Butler : Question #92


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5!-3! = 5*4*3*2*1-3*2=3*2(5*4-1) = 6*19=114. This probably is a sub 600 level question though, not 600-700.
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Re: For a positive integer n, the number n! is defined to be [#permalink] New post   15 Jun 2023, 04:22
For a positive integer n, the notation n! represents the factorial of n. The factorial of a positive integer n is calculated by multiplying all positive integers from 1 to n together.

Mathematically, n! can be defined as:

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

For example, if n = 5, then 5! (read as "5 factorial") would be calculated as:

5! = 5 × 4 × 3 × 2 × 1 = 120

In general, n! grows very quickly as n increases. The factorial function is commonly used in various mathematical calculations, combinatorics, and probability theory.
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Re: For a positive integer n, the number n! is defined to be [#permalink]
15 Jun 2023, 04:22
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