Factorials

Number Theory Level 1

If a ! ( b − 1 ) ! = 60 \dfrac{a!}{(b-1)!}= 60 and ( a − 1 ) ! b ! = 4 \dfrac{(a-1)!}{b!} = 4 , what is the value of a × b a\times {b} ?


The answer is 15.

Christopher Boo by Christopher Boo , 24, Singapore

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2 solutions

a ! ( b − 1 ) ! = 60 a ! = 60 ⋅ ( b − 1 ) ! . . . ( 1 ( a − 1 ) ! b ! = 4 ( a − 1 ) ! = 4 b ! . . . ( 2 ( 1 ( 2 = a ! ( a − 1 ) ! = 60 ⋅ ( b − 1 ) ! 4 b ! a = 15 b a b = 15 \frac { a! }{ (b-1)! } =60\\ a!=60\cdot (b-1)!...(1\\ \frac { (a-1)! }{ b! } =4\\ (a-1)!=4b!...(2\\ \frac { (1 }{ (2 } =\\ \frac { a! }{ (a-1)! } =\frac { 60\cdot (b-1)! }{ 4b! } \\ a=\frac { 15 }{ b } \\ ab=15

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I think the answer would be 1 on the grounds that 15 = 1.

A W - 3 years, 10 months ago
Richard Costen
Jul 9, 2017

Divide equation 1 by equation 2, which simplifies to a b = 15 ab=15 .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

a × b a \times b is equivalent to a b ab notation-wise. :)

Michael Huang - 3 years, 11 months ago

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Before Christopher changed it, the question was "What is the value of a b \displaystyle \frac ab ?"

Zach Abueg - 3 years, 11 months ago

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Ah. Didn't see that coming. Thanks!

Michael Huang - 3 years, 11 months ago

We will actually get 'a' equals 5 and 'b' equals 3.

genis dude - 3 years, 11 months ago

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