In one lottery game, contestants pick five numbers from 1 through 40 and have to match all five for the big prize (in any order). You'll get second prize if you match four of the five numbers. Find the probability of winning second prize if you buy five tickets.

Question

In one lottery game, contestants pick five numbers from 1 through 40 and have to match all five for the big prize (in any order). You'll get second prize if you match four of the five numbers.  Find the probability of winning second prize if you buy five tickets.

anonymous · Answer

you have to pick four out of the five numbers correctly, is that right?

anonymous · Answer

the number of ways to choose 5 out of 40 numbers is $$\binom{40}{5}$$ 
that is your denominator
you may have seen this written as $$_{40}C_5$$

anonymous · Answer

your numerator is the number of ways to choose 4 out of 5, i.e $\binom{5}{4}$ which is $5$ times the number of ways to choose a wrong number which is 35 (since there are 40 total and 5 are winners

anonymous · Answer

Why is the numerator (# of ways of choosing a winner) * (number of ways of choosing a looser)?

anonymous · Answer

you have 4 winners not 5
that means there is a loser in there

anonymous · Answer

the numerator is the number of ways you can choose 4 winners out of 5, times the number of ways you can choose one loser out of 35

anonymous · Answer

in other words it is $$5\times 35$$

anonymous · Answer

I'm not getting the 35

anonymous · Answer

5 are good
there are 40 all together
how many are not good?

anonymous · Answer

Yeah, I get that 40 - 5 = 35.  I was struggling with why I needed another factor in the numerator.  I get it now.  Thanks.

anonymous · Answer

yw