Wierd Math with Crazy Logic

Number Theory Level 1

If 1 ! = 1 1!=1 , then find the value of 0 ! 0! .


The answer is 1.

Terry Yu by Terry Yu , 17, USA

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2 solutions

Terry Yu
May 4, 2017

With permutations, we made a formula involving n ! k ! ( n − k ) ! \frac{n!}{k!(n-k)!} with n and k being the number of ways of choosing k things from a collection of n things. If there was a problem that if there was 2 people, how many handshakes could be made? when n = k = 2 n=k=2 . Then the equation will be 2 ! 2 ! ( 0 ) ! = 1 \frac{2!}{2!(0)!}=1 . That means that 0 ! 0! must be 1 1 for the equation to work. □ \square

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Zach Abueg
May 5, 2017

n ! n! can be thought of as the number of ways to arrange n n objects. Intuitively, there is 1 1 way to arrange a set of 0 0 objects.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

if you had 0 objects, then wouldn't you not be able to arrange at all? I mean, if I didn't have a pencil, I can't arrange a pencil since I don't have one.

Terry Yu - 4 years, 1 month ago

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