Question

To win a certain state lottery, players must correctly choose 4 numbers (in any order) from the numbers 1 to 40. How many different 4 number combinations are there? A. 800 B. 91390 C. 160 D. 24

Answer 1

theres about 800 different combinations, i'm not sure though, i'm sorry if i'm wrong

Answer 2

Answer: B. 91,390

Explanation:

The combination of n things taken m things at a time is given by :-

`^nC_m=(n!)/(m!(n-m)!)`

Given : The total numbers in lottery = 40

The number of correct numbers to win the lottery = 4

Now, the combination of 40 numbers taken 4 correct numbers at a time is given by :-

`^(40)C_(4)=(40!)/(4!(40-4)!)\\\\=(40*39*38*37*36!)/((24)(36!))=91,390`

Hence, there are 91,390 different 4 number combinations .