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

Answer:  B. 91,390

Step-by-step explanation:

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

$^nC_m=\dfrac{n!}{m!(n-m)!}$

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 :-

$^{40}C_{4}=\dfrac{40!}{4!(40-4)!}\\\\=\dfrac{40\times39\times38\times37\times36!}{(24)(36!)}=91,390$

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

Answer 2

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