Final answer:
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.