what is the probability of winning assuming that the order is unimportant when I must choose 4 numbers from the numbers 1 through 17

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

1/17 * 1/16 * 1/15 * 1/14 = ?

To calculate the probability of winning when choosing 4 numbers from a set of 17 numbers, we can use combinations. Since the order is unimportant, we can directly use the formula for combinations.

The formula for combinations is:
C(n, r) = n! / (r! * (n-r)!)

In this case:
n = total number of numbers = 17
r = number of numbers to be chosen = 4

Plugging in the values, the calculation becomes:
C(17, 4) = 17! / (4! * (17-4)!)

Simplifying the expression:
C(17, 4) = 17! / (4! * 13!)

To solve, we can expand the factorials:
C(17, 4) = (17 * 16 * 15 * 14 * 13!) / (4 * 3 * 2 * 1 * 13!)

Simplifying further:
C(17, 4) = (17 * 16 * 15 * 14) / (4 * 3 * 2 * 1)

Evaluating the expression:
C(17, 4) = 2380

Therefore, the probability of winning when choosing 4 numbers from the numbers 1 through 17, assuming the order is unimportant, is 1 in 2380.

To calculate the probability of winning when the order is unimportant, we need to use the concept of combinations. A combination is a selection of items from a larger set, where the order does not matter.

In this scenario, you need to choose 4 numbers from a set of 17 numbers (1 through 17). The formula to calculate combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where:
n is the total number of items to choose from
r is the number of items to choose without repetition
! denotes the factorial operation (the product of an integer and all the positive integers below it)

Using this formula, we can calculate the number of possible combinations of choosing 4 numbers from 17:

C(17, 4) = 17! / (4! * (17-4)!)
= (17 * 16 * 15 * 14) / (4 * 3 * 2 * 1)
= 2380

There are 2380 different combinations of choosing 4 numbers from the set of 17 numbers.

Now, to calculate the probability of winning, we need to determine the favorable outcomes, which is 1 (since there is only one winning combination) and divide it by the total number of possible outcomes:

Probability of winning = 1 / 2380

Hence, the probability of winning is approximately 0.00042 or 0.042%.