Question

To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of 51 numbers​ (1 through ​). 51 The order in which the selection is made does not matter. How many different selections are​ possible?

Answer 1

Answer:

249,900

Step-by-step explanation:

This is called selecting a combination of 4 numbers from 51. In math, it is called a combination because the order you pick them in does not matter.

The formual for this is:

for a combination of 'n' things taken 'r' at a time,

nCr = n! ÷ { r!(n -r)! }

Part of understanding this is knowing what n! means.

It is called "n factorial" and is n * n-1 * n-2 * n-3 * ... until you get down to 3 * 2 * 1.

So 5!, for instance, is 5*4*3*2*1 = 120

For this example,

51 C 4 = 51! ÷ {4! 47! }

If you do this on a calculator, by figururing all the factorials and doing the dividing, you get insanely big numbers for 51! and 47!

Most calculators do have a way to solve these problems without you really doing any of the math, but you should understand the math first.

So you can do it manually, like in the picture I attached.

You should get 5,997,600 ÷ 24 = 249,900

Hope this helps