Question

1. in the california state lottery, you must select six numbers from fifty - two numbers to win the big prize. the numbers do not have to be in a particular order. what is the probability that you will win the big prize if you buy one ticket?

$_{n}c_{r}=\frac{n!}{r!(n - r)!}$
$_{52}c_{6}=$

Explanation:

Step1: Identify combination formula

We use the combination formula \( _nC_r=\frac{n!}{r!(n - r)!} \), where \( n = 52 \) (total numbers) and \( r = 6 \) (numbers to select).

Step2: Calculate \( _{52}C_6 \)

Substitute \( n = 52 \) and \( r = 6 \) into the formula:

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Step3: Find probability

There is 1 winning combination, so the probability \( P=\frac{1}{_{52}C_6}=\frac{1}{20358520} \)

Answer:

The probability is \(\frac{1}{20358520}\) (or approximately \(4.91\times10^{-8}\))