Calculate the probability of choosing 3 green marbles out of 10 selected using combinations.
Probability of Choosing Green Marbles:
To calculate the probability of choosing exactly 3 green marbles out of 10 selected, you can use combinations. There are \[tex]\({{15 \\choose 3} \\cdot {35 \\choose 7}}\\)[/tex] ways to choose 3 green marbles from 15 and 7 non-green marbles from the remaining 35. The total number of ways to choose 10 marbles out of 50 is \[tex]\({{50 \\choose 10}}\\)[/tex]. Therefore, the probability is \[tex]\({{15 \\choose 3} \\cdot {35 \\choose 7}} / {50 \\choose 10}\\)[/tex].
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