A box contains 5 green balls, 6 orange balls and 4 pink balls. Three balls are drawn at random. In how many ways can the 3 balls be drawn from 15 balls24. if the color is not considered? 25. 1 ball from each color?26. 2 green balls and 1 pink ball?27. 3 green or orange balls? 28. if all three balls are orange?
Question
A box contains 5 green balls, 6 orange balls and 4 pink balls. Three balls are drawn at random. In how many ways can the 3 balls be drawn from 15 balls24. if the color is not considered? 25. 1 ball from each color?26. 2 green balls and 1 pink ball?27. 3 green or orange balls? 28. if all three balls are orange?
Solution
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The total number of balls is 5 (green) + 6 (orange) + 4 (pink) = 15 balls. The number of ways to draw 3 balls from 15, without considering the color, is given by the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose. So, C(15, 3) = 15! / [(15-3)! * 3!] = 455 ways.
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To draw 1 ball from each color, we have 5 ways to choose a green ball, 6 ways to choose an orange ball, and 4 ways to choose a pink ball. So, the total number of ways is 5 * 6 * 4 = 120 ways.
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To draw 2 green balls and 1 pink ball, we have C(5, 2) ways to choose the green balls and C(4, 1) ways to choose the pink ball. So, the total number of ways is C(5, 2) * C(4, 1) = 10 * 4 = 40 ways.
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To draw 3 green or orange balls, we have C(11, 3) ways, where 11 is the total number of green and orange balls. So, the total number of ways is C(11, 3) = 165 ways.
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To draw all three balls as orange, we have C(6, 3) ways, where 6 is the total number of orange balls. So, the total number of ways is C(6, 3) = 20 ways.
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