# `!` — Factorial / Binomial

Function. Ranks: `0` monadic, `0 0` dyadic

`!Y`: Y!. Pervasive.

``` bpl
!5                ⍝ 120
!5ₓ               ⍝ 120ₓ
```

`X!Y`: binomial coefficient, Y choose X. Pervasive.

``` bpl
2!5               ⍝ 10
2ₓ!5ₓ             ⍝ 10ₓ
```

Extends through Gamma to non-integral and complex arguments. At a pole,
a negative integer, the result is an infinity or NaN, as the gamma
function gives it.