Final answer:
To determine the number of different sets of 5 numbers that can be chosen from 1 to 53, the combinations formula C(n, r) = n! / (r! * (n-r)!) is used. It is found that there are C(53, 5) different combinations possible.
Step-by-step explanation:
To find the number of different sets of 5 numbers that can be chosen, we can use the concept of combinations. Since order doesn't matter, we use combinations instead of permutations. In this case, we have 53 numbers to choose from and we need to select 5 numbers.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items we want to select.
Using this formula, we can calculate:
C(53, 5) = 53! / (5!(53-5)!) = 53! / (5!48!) = (53 * 52 * 51 * 50 * 49) / (5 * 4 * 3 * 2 * 1) = 53 * 52 * 51 * 50 * 49 = 258,271,200
Therefore, there are 258,271,200 different sets of 5 numbers that can be chosen from 1 to 53 inclusive.