Question

In a lottery, 5 different numbers are chosen from the first 90 positive integers. How many different combinations of numbers are possible?

1) 90
2) 120
3) 150
4) 180

Answer 1

The number of different combinations of 5 numbers from the first 90 integers is calculated using the combinations formula and is found to be 43,949,268, which does not match any of the options provided.

Step-by-step explanation:

In order to determine how many different combinations of 5 numbers can be chosen from the first 90 positive integers, we use the formula for combinations without repetition, which is given by C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, and k is the number of items to choose. Using this formula, we calculate C(90, 5) = 90! / (5! * (90 - 5)!) = 90! / (5! * 85!) = (90 * 89 * 88 * 87 * 86) / (5 * 4 * 3 * 2 * 1), after cancelling out the common factorial terms.

After the calculation, we find that the number of combinations is 43,949,268, which is not one of the options listed in the original question, indicating a possible error in the question or the provided options.