Question

among a set of 5 green balls and 3 blue balls, how many selections of 5 balls can be made such that at least 3 of them are green balls

Answer 1

46 selections

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We want to find the number of combinations for the following scenarios:

• selecting 3 green balls and 2 blue balls,
• selecting 4 green balls and 1 blue ball, and
• selecting all 5 green balls.

For 3 green and 2 blue:

• There are C(5,3) ways to choose 3 green balls and C(3,2) ways to choose 2 blue balls.

For 4 green and 1 blue:

• There are C(5,4) ways to choose 4 green balls and C(3,1) ways to choose 1 blue ball.

For all 5 green:

• There is C(5,5)  ways to choose all green balls.

We sum up all these possibilities to find the total number of combinations that satisfy the condition of having at least 3 green balls in the selection:

• C(5,3) * C(3,2) + C(5,4) * C(3,1) + C(5,5) =
• 10*3 + 5*3 + 1 =
• 30 + 15 + 1 =
• 46