PROBABILITY HELP!!!!!!

to play a lottery game, you choose six different numbers between 1 and 40.

show that the probability of choosing all six numbers correctly is about 1 in 4 million

please show me how you get the answer

thank you

You use the binomial theorem, nCr. Read as n Choose r, in this case you pick 6 from 40. You can use a calculator with an nCr function, or calculate it yourself using the factorial formula:

P = nCr = (n!)/(r!*(n-r)!) = (40!)/(6!*34!) = 3838380 (very close to 4 million).

In case you don't know what ! means, it means factorial. So
3! = 3 x 2 x 1 = 6
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
etc

p (any number) = 1/40

therefore you want to times 1/40 by itself 6 times to get =

This = 1/2.4414x10^+10

so that's 1
24414000000

which is about 1 in 4 million! :)