Question

To win at LOTTO in one​ state, one must correctly select 5 numbers from a collection of numbers​ (1 through 51​). The order in which the selection is made does not matter. How many different selections are​ possible?

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \boxed{\text{$\sf C_((n,p)) = (n!)/(p!\:.\:(n - p)!)$}}`

`\Large \text{$\sf C_((51,5)) = (51!)/(5!\:.\:(51 - 5)!)$}`

`\Large \text{$\sf C_((51,5)) = (51.50.49.48.47.46!)/(5!\:.\:46!)$}`

`\Large \text{$\sf C_((51,5)) = (51.50.49.48.47)/(120)$}`

`\Large \text{$\sf C_((51,5)) = (281.887.200)/(120)$}`

`\Large \boxed{\boxed{\text{$\sf C_((51,5)) = 2.349.060$}}}`