Question

City lottery, selecting 4 numbers from 1 to 24. How many ways can you select 4 numbers?

A. 10,626
B. 106,920
C. 26,460
D. 70,560

Answer 1

The number of ways to select 4 numbers from 1 to 24 in a city lottery is calculated using combinations. The correct calculation is C(24, 4) = 24! / [4! * (24 - 4)!], which equals 10,626. Therefore, option A is the correct answer.

Step-by-step explanation:

To calculate the number of ways you can select 4 numbers from 1 to 24, we use the formula for combinations, not permutations, because the order in which the numbers are drawn does not matter. The combination formula is given by:

C(n, k) = n! / [k! * (n - k)!]

where:

• n is the total number of items,
• k is the number of items to choose,
• n! is the factorial of n,
• k! is the factorial of k.

For this question:

• n = 24 (since there are 24 numbers to choose from),
• k = 4 (since we are choosing 4 numbers).

Using the formula, we get:

C(24, 4) = 24! / [4! * (24 - 4)!] = (24 * 23 * 22 * 21)/(4 * 3 * 2 * 1)

This simplifies to:

C(24, 4) = (24 * 23 * 22 * 21) / (4 * 3 * 2 * 1) = 10,626

Therefore, there are 10,626 ways to select 4 numbers from 1 to 24, which corresponds to option A.