Question 1

13,983,816 different tickets are possible.

The number of different lottery tickets possible when selecting 6 distinct numbers from a set of 49 is 13,983,816. This is calculated using the combination formula, which accounts for the fact that order does not matter in this selection.

A) 1,176,720

Option A is incorrect because it reflects the number of ways to choose 6 numbers from a smaller set. It does not account for the full range of 49 numbers, leading to a significant underestimation of the possibilities.

B) 7,059,052

Option B is also incorrect as it undercounts the total combinations. This number does not follow the combination formula for selecting 6 from 49, hence it does not represent the correct calculation.

C) 13,983,816

Option C is correct because it accurately uses the combination formula, denoted as C(49, 6), which equals 49! / (6! * (49-6)!), yielding exactly 13,983,816 possible combinations.

D) 49,000

Option D is incorrect; it significantly underestimates the number of possible combinations. This figure does not relate to the computation of combinations for selecting 6 from 49, making it an unsuitable answer.

Conclusion

The correct answer, 13,983,816, is derived from the proper application of the combination formula, demonstrating the vast number of distinct lottery tickets possible from a set of 49 numbers. All other options fail to correctly calculate or represent the combinations, thus confirming that C is the definitive answer.