Answer: 120
Step-by-step explanation:
Since the order of the numbers doesn't matter we can use the formula:
[tex]\dfrac{n!}{r!(n-r)!}\quad \text{where n is the quantity of items and r is the quantity chosen}\\\\\text{In this problem, there are 10 numbers (n = 10) and 7 to be chosen (r = 7)}\\\\_{10}C_{7}=\dfrac{10!}{7!(10-7)!}\\\\.\qquad=\dfrac{10!}{7!3!}\\\\.\qquad=\dfrac{10\times 9\times 8\times 7!}{7!\times 3\times 2\times 1}\\\\.\qquad=10\times 3\times 4\\\\.\qquad=120[/tex]
Probability helps us to know the chances of an event occurring. The probability of Choosing the 7 winning lottery numbers when the numbers are chosen at random from 0 to 9 is 0.000504.
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Choosing the 7 winning lottery numbers when the numbers are chosen at random from 0 to 9. Therefore, the total number of possible outcomes is,
Total possible options = 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10⁷
Now, the number of ways to choose the winning numbers is,
Number of required cases = 7×6×5×4×3×2×1 = 5040
Further, the probability can be written as,
Probability = 5040/10⁷ = 0.000504
Hence, the probability of Choosing the 7 winning lottery numbers when the numbers are chosen at random from 0 to 9 is 0.000504.
Learn more about Probability:
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