Answer:
[tex]48C7=73,629,072\ ways[/tex]
Step-by-step explanation:
Since the order in which you select the numbers is not important then we have a combination problem
The formula of combinations is:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of objects you can choose, and you choose r from them
Then you will get the number of possible ways to select r objects from a group of n objects
In this case we have that:
[tex]n=48\\\\r=7[/tex]
Therefore:
[tex]48C7=\frac{48!}{7!(48-7)!}[/tex]
[tex]48C7=\frac{48!}{7!*41!}[/tex]
[tex]48C7=\frac{48*47*46*45*44*43*42*41!}{7*6*5*4*3*2*1*41!}[/tex]
[tex]48C7=\frac{48*47*46*45*44*43*42}{7*6*5*4*3*2*1}[/tex]
[tex]48C7=73,629,072\ ways[/tex]
