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Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816?
Most Upvoted Answer
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls...
Solution:
Understanding the problem:
We need to choose 10 balls in such a way that each box provides at least 1 red and 1 blue ball. This means that we can choose 2 red and 1 blue ball or 1 red and 2 blue balls from each box.
Approach:
We can solve this problem using combinatorics. We will choose 2 red balls and 1 blue ball or 1 red ball and 2 blue balls from each box to get a total of 10 balls. Let's solve this problem step by step.
Step 1: Find the total number of ways to choose 10 balls from 20 balls without any restrictions.
We can choose 10 balls from 20 balls in 20C10 ways.
20C10 = 184,756
Step 2: Find the number of ways to choose 10 balls from 20 balls such that at least 1 red and 1 blue ball are chosen from each box.
Let's consider the following cases:
Case 1: Choose 2 red and 1 blue ball from each box.
We need to choose 2 red and 1 blue ball from each box. This means that we need to choose a total of 8 red balls and 4 blue balls.
Number of ways to choose 8 red balls from 12 red balls = 12C8
Number of ways to choose 4 blue balls from 8 blue balls = 8C4
Total number of ways to choose 8 red and 4 blue balls = 12C8 * 8C4
Similarly, we can choose 1 red and 2 blue balls from each box.
Case 2: Choose 1 red and 2 blue ball from each box.
We need to choose 1 red and 2 blue ball from each box. This means that we need to choose a total of 4 red balls and 6 blue balls.
Number of ways to choose 4 red balls from 12 red balls = 12C4
Number of ways to choose 6 blue balls from 8 blue balls = 8C6
Total number of ways to choose 4 red and 6 blue balls = 12C4 * 8C6
Step 3: Add the number of ways in Case 1 and Case 2.
Total number of ways to choose 10 balls from 4 boxes such that each box provides at least 1 red and 1 blue ball = 12C8 * 8C4 + 12C4 * 8C6
= 21816
Answer: Therefore, the correct option is (1) 21816.
Understanding the problem:
We need to choose 10 balls in such a way that each box provides at least 1 red and 1 blue ball. This means that we can choose 2 red and 1 blue ball or 1 red and 2 blue balls from each box.
Approach:
We can solve this problem using combinatorics. We will choose 2 red balls and 1 blue ball or 1 red ball and 2 blue balls from each box to get a total of 10 balls. Let's solve this problem step by step.
Step 1: Find the total number of ways to choose 10 balls from 20 balls without any restrictions.
We can choose 10 balls from 20 balls in 20C10 ways.
20C10 = 184,756
Step 2: Find the number of ways to choose 10 balls from 20 balls such that at least 1 red and 1 blue ball are chosen from each box.
Let's consider the following cases:
Case 1: Choose 2 red and 1 blue ball from each box.
We need to choose 2 red and 1 blue ball from each box. This means that we need to choose a total of 8 red balls and 4 blue balls.
Number of ways to choose 8 red balls from 12 red balls = 12C8
Number of ways to choose 4 blue balls from 8 blue balls = 8C4
Total number of ways to choose 8 red and 4 blue balls = 12C8 * 8C4
Similarly, we can choose 1 red and 2 blue balls from each box.
Case 2: Choose 1 red and 2 blue ball from each box.
We need to choose 1 red and 2 blue ball from each box. This means that we need to choose a total of 4 red balls and 6 blue balls.
Number of ways to choose 4 red balls from 12 red balls = 12C4
Number of ways to choose 6 blue balls from 8 blue balls = 8C6
Total number of ways to choose 4 red and 6 blue balls = 12C4 * 8C6
Step 3: Add the number of ways in Case 1 and Case 2.
Total number of ways to choose 10 balls from 4 boxes such that each box provides at least 1 red and 1 blue ball = 12C8 * 8C4 + 12C4 * 8C6
= 21816
Answer: Therefore, the correct option is (1) 21816.
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Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816?
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Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816?.
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816?.
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Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816?, a detailed solution for Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? has been provided alongside types of Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen? 1. 21816 2. 85536 3. 12096 4. 156816? theory, EduRev gives you an
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