Question

California Lottery has now allowed its residents to join Powerball Lottery. In how many ways can you select 5 numbers from a choice of the numbers 1 thru 59. Show calculation using the C(n,k) formula.

Answer 1

Answer: 5006386

Explanation:

Given : The total numbers in California Lottery from 1 through 59 = 59

The numbers need to select = 5

We know that the number of combination of n things taken r at a time is given by :-

`^nC_r=(n!)/(r!(n-r)!)`

Now, the number of combination of 59 things taken 5 at a time is given by :-

`^(59)C_5=(59!)/(5!(59-5)!)\\\\=(59*58*57*56*55*54!)/((120)54!)\\\\=5006386`

Hence, the number of combination of 59 things taken 5 at a time is =5006386