Math Problem Statement
The bag contains 3 red, 2 green, 1 purple, 2 yellow, and 2 orange marbles.Find the number of sets of picking up 4 marbles at a time that contain all the red marbles available.
Solution
To find the number of sets of picking up 4 marbles that contain all the 3 red marbles, we need to first consider that 3 of the 4 marbles are already determined (they must be red). This leaves us with the task of choosing 1 additional marble from the remaining non-red marbles.
Here's the breakdown:
- Number of red marbles: 3 (which must be included in the set).
- Total number of non-red marbles: .
These 7 non-red marbles consist of:
- 2 green
- 1 purple
- 2 yellow
- 2 orange
Now, we need to choose 1 marble from these 7 non-red marbles.
The number of ways to choose 1 marble from 7 is calculated as follows:
Thus, the number of sets of picking up 4 marbles that contain all 3 red marbles is 7.
Would you like more details on this calculation or have any other questions?
Here are 5 related questions:
- How would the result change if there were only 2 red marbles?
- What if you were asked to pick 5 marbles containing all the red ones?
- How many sets of 4 marbles can be picked if the set must include exactly 2 red marbles?
- What is the probability of picking a set of 4 marbles that includes all the red ones?
- How does the number of sets change if more colors or marbles were added?
Tip: When dealing with combinations, it helps to separate the problem into smaller steps—first fixing the required items, then considering the choices left for the remaining items.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
Combination formula: C(n, k) = n! / (k! * (n - k)!)
Theorems
-
Suitable Grade Level
High School
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