Answer:
The number of ways to choose these three red balls is given by the combination formula C(55, 1) * C(54, 1) * C(53, 1). To find the total number of ways, we add up the results from these three scenarios: Total number of ways = C(77, 2) + C(55, 1) * C(54, 1) * C(77, 1) + C(55, 1) * C(54, 1) * C(53, 1) Calculating these combinations will give us the final answer. There are 54 options remaining for choosing the second red ball. - There are 53 options remaining for choosing the third red ball.
Explanation:
To find the number of ways three balls can be drawn from the box if at least one red ball is to be included in the draw, we can consider the different scenarios: 1. Drawing exactly one red ball: - There are 55 options for choosing one red ball. - There are 77 options remaining (33 white balls + 44 black balls). - The number of ways to choose two balls from these 77 options is given by the combination formula C(77, 2). 2. Drawing exactly two red balls: - There are 55 options for choosing the first red ball. - There are 54 options remaining for choosing the second red ball. - There are 77 options remaining for choosing the third ball. - The number of ways to choose these two red balls and one additional ball is given by the product C(55, 1) * C(54, 1) * C(77, 1). 3. Drawing all three red balls: - There are 55 options for choosing the first red ball.