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A bag contains n white and n black balls (all different). Pairs of balls are drawn one-by-one without replacement until the bag is empty. If the number of ways to draw the balls in which each pair consists of one black and one white ball is 576, then the value of n is equal to__
Correct answer is '4'. Can you explain this answer?
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A bag contains n white and n black balls (all different). Pairs of ba...
Solution:
Let's assume that the bag contains n white balls and n black balls.
To find the number of ways to draw the balls in which each pair consists of one black and one white ball, we need to consider the arrangement of the balls.
Number of ways to choose the first pair: n black balls * n white balls = n^2
After choosing the first pair, there will be (n-1) white balls and (n-1) black balls left in the bag.
Number of ways to choose the second pair: (n-1) black balls * (n-1) white balls = (n-1)^2
Similarly, for the third pair, the number of ways to choose: (n-2) black balls * (n-2) white balls = (n-2)^2
Continuing this process, we can determine the number of ways to choose each pair until the bag is empty.
So, the total number of ways to draw the balls in which each pair consists of one black and one white ball is:
n^2 * (n-1)^2 * (n-2)^2 * ... * 2^2 * 1^2
This can be written as n!^2, where n! denotes the factorial of n.
Given that the number of ways is 576, we have:
n!^2 = 576
Taking the square root on both sides, we get:
n! = sqrt(576)
n! = 24
Now, we need to find the value of n.
By checking the factorials of numbers from 1 to 10, we can see that 4! = 24.
Therefore, the value of n is 4.
Hence, the correct answer is 4.
Let's assume that the bag contains n white balls and n black balls.
To find the number of ways to draw the balls in which each pair consists of one black and one white ball, we need to consider the arrangement of the balls.
Number of ways to choose the first pair: n black balls * n white balls = n^2
After choosing the first pair, there will be (n-1) white balls and (n-1) black balls left in the bag.
Number of ways to choose the second pair: (n-1) black balls * (n-1) white balls = (n-1)^2
Similarly, for the third pair, the number of ways to choose: (n-2) black balls * (n-2) white balls = (n-2)^2
Continuing this process, we can determine the number of ways to choose each pair until the bag is empty.
So, the total number of ways to draw the balls in which each pair consists of one black and one white ball is:
n^2 * (n-1)^2 * (n-2)^2 * ... * 2^2 * 1^2
This can be written as n!^2, where n! denotes the factorial of n.
Given that the number of ways is 576, we have:
n!^2 = 576
Taking the square root on both sides, we get:
n! = sqrt(576)
n! = 24
Now, we need to find the value of n.
By checking the factorials of numbers from 1 to 10, we can see that 4! = 24.
Therefore, the value of n is 4.
Hence, the correct answer is 4.
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Community Answer
A bag contains n white and n black balls (all different). Pairs of ba...
Number of ways to draw 1st pair = (nC1× nC1)
Number of ways to draw 2nd pair = (n−1C1× n−1C1)
Number of ways to draw 3rd pair =(n−2C1× n−2C1)
Number of ways to draw last i.e., nth pair = (1C1× 1C1)
Combining all the above results, we get
Number of ways to draw n pairs
⇒ n2(n−1)2...22 × 12 = (24)2
⇒ (n!)2 = (24)2
⇒ n! = 24 = 4!
∴ n = 4
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A bag contains n white and n black balls (all different). Pairs of balls are drawn one-by-one without replacement until the bag is empty. If the number of ways to draw the balls in which each pair consists of one black and one white ball is 576, then the value of n is equal to__Correct answer is '4'. Can you explain this answer?
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A bag contains n white and n black balls (all different). Pairs of balls are drawn one-by-one without replacement until the bag is empty. If the number of ways to draw the balls in which each pair consists of one black and one white ball is 576, then the value of n is equal to__Correct answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A bag contains n white and n black balls (all different). Pairs of balls are drawn one-by-one without replacement until the bag is empty. If the number of ways to draw the balls in which each pair consists of one black and one white ball is 576, then the value of n is equal to__Correct answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains n white and n black balls (all different). Pairs of balls are drawn one-by-one without replacement until the bag is empty. If the number of ways to draw the balls in which each pair consists of one black and one white ball is 576, then the value of n is equal to__Correct answer is '4'. Can you explain this answer?.
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