Question

To win a loto in one state, one must correctly select 7 numbers from a collection of 48 numbers (1 through 48). The order in which the selection is made does not matter. How many different selections are possible?

Answer 1

Answer:

$48C7=73,629,072\ ways$

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:

$nCr=\frac{n!}{r!(n-r)!}$

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:

$n=48\\\\r=7$

Therefore:

$48C7=\frac{48!}{7!(48-7)!}$

$48C7=\frac{48!}{7!*41!}$

$48C7=\frac{48*47*46*45*44*43*42*41!}{7*6*5*4*3*2*1*41!}$

$48C7=\frac{48*47*46*45*44*43*42}{7*6*5*4*3*2*1}$

$48C7=73,629,072\ ways$