Lottery how many possible number combinations

In order to win the second prize, five of the six numbers on the ticket must match five of the six winning numbers; in other words, we must have chosen five of the six winning numbers and one of the 42 losing numbers. So the probability of winning the second prize is.

A multiple-choice question on an economics quiz contains 10 questions with five possible answers each. Compute the probability of randomly guessing the answers and getting 9 questions correct. In many card games such as poker the order in which the cards are drawn is not important since the player may rearrange the cards in his hand any way he chooses ; in the problems that follow, we will assume that this is the case unless otherwise stated.

Thus we use combinations to compute the possible number of 5-card hands, 52 C 5. This number will go in the denominator of our probability formula, since it is the number of possible outcomes. For the numerator, we need the number of ways to draw one Ace and four other cards none of them Aces from the deck. Since there are four Aces and we want exactly one of them, there will be 4 C 1 ways to select one Ace; since there are 48 non-Aces and we want 4 of them, there will be 48 C 4 ways to select the four non-Aces.

The solution is similar to the previous example, except now we are choosing 2 Aces out of 4 and 3 non-Aces out of 48; the denominator remains the same:. It is useful to note that these card problems are remarkably similar to the lottery problems discussed earlier.

And then let's see, 15 divided by 3 is 5. And let's see, we have a 58 divided by 2 is So our answer is going to be 5 times 59, times 29, times Now this isn't going to be our answer. This is going to be the number of combinations we can get if we choose four numbers out of 60 and we don't care about order.

So let's take the calculator out now. So we have 5 times 59, times 29, times It's equal to , So let me write that down.

That is , combinations. If you're picking four numbers, you're choosing four numbers out of 60, or 60 choose four. Now, the question they say is, what is the probability that the winning numbers are 3, 15, 46, and 49? Well, this is just one particular of the combinations. This is just one of the , possible outcomes. So the probability of 3, 15, 46, 49 winning is just equal to-- well, this is just one of the outcomes out of , So that right there is your probability of winning.

Nearly tripling your investment on a guaranteed jackpot sounds pretty good, doesn't it? Here's the problem. While you can guarantee a jackpot win, you can't guarantee that you'll end up with a profit. Even with an advertised jackpot bigger than the amount you'd have to invest, there are costs that eat into your earnings.

Here are some of the reasons why guaranteeing a lottery win doesn't make sense. First of all, you might have to split the jackpot with other winners. But you have to do more than simple math to find out the profit you'll make when you win the lottery. For one thing, you have to pay taxes on those winnings. Next, you have to consider whether you'll take the lump-sum or annuity payout. You'll only get the full advertised amount of the jackpot if you take the annuity option — which means that you have to wait 30 years until you see your return on investment.

There are many other ways to invest half a million dollars that could be more profitable and offer more liquidity. If you take the lump-sum payout, you'll receive significantly less money.

Finally, there are a number of things that you should do before you cash in a major lottery win , including hiring lawyers and accountants to protect your interests. Hiring good people is important, but it costs money, further eating into your jackpot profits. But jackpots can grow ever larger than that, can't they?

Well, kind of, but not really. As jackpot values rise, lottery fever kicks in and more and more people buy tickets. The more tickets sold, the higher the chances that all possible combinations will be covered. So before the jackpots get close to big enough to be worth buying all the tickets, someone will almost certainly buy a winning ticket. Powerball recently changed its drawing setup. These days, a machine sucks up five white balls from a bin of 69 balls, each with a different number.

It also sucks up one red Powerball from a bin of 26 different balls. To take home the jackpot, your ticket must have the same five white numbers — order doesn't matter — and the one red number.

If you do the math , there are 11,, possible combinations of five white balls without order mattering. Multiply that by the 26 possible red balls, and you get ,, possible Powerball number combinations. The Powerball draws only twice a week: Every Wednesday and Saturday. So how are you going to print that many tickets in less than four days? Even if you can cram multiple picks onto one ticket?