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If x, y, and z are integers and x > 0, y > 1, z > 2, x+y + z= 15 then the number of values of the ordered triplet (x, y, z) is
- a)91
- b)455
- c)17C15
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If x, y, and z are integers and x > 0, y > 1, z > 2, x+y +...
H ere, Since x > 0 , y > l , z > 2
Now, x can get any number of things, y should get a minimum of 1 thing and z should get a minimum of 2 things. So, let us give these to y and z.
Now , total things left = 12
Now , total things left = 12
Now use the formula n identical things can be distributed among r persons in n+x-1Cx-1
Where n = 12, r = 3
Most Upvoted Answer
If x, y, and z are integers and x > 0, y > 1, z > 2, x+y +...
However, I can provide a logical explanation of the problem.
From the given inequality, we know that x is less than y, and y is less than z. Thus, z is the largest among the three integers, and x is the smallest.
Let's assume that x = 1. Then, y can take any integer value between 2 and z-1, and z can take any integer value greater than y.
Therefore, the number of possible solutions for the inequality is the sum of the number of integers between 2 and z-1, for all possible values of z greater than 2. We can represent this mathematically as:
∑(z-2), where the summation is taken from z=3 to infinity.
Using the formula for the sum of an arithmetic series, we can simplify this expression as:
∑(z-2) = ∞/2 * (3 + ∞-1) = ∞/2 * ∞ = ∞
Therefore, the number of possible solutions for the inequality is infinity.
From the given inequality, we know that x is less than y, and y is less than z. Thus, z is the largest among the three integers, and x is the smallest.
Let's assume that x = 1. Then, y can take any integer value between 2 and z-1, and z can take any integer value greater than y.
Therefore, the number of possible solutions for the inequality is the sum of the number of integers between 2 and z-1, for all possible values of z greater than 2. We can represent this mathematically as:
∑(z-2), where the summation is taken from z=3 to infinity.
Using the formula for the sum of an arithmetic series, we can simplify this expression as:
∑(z-2) = ∞/2 * (3 + ∞-1) = ∞/2 * ∞ = ∞
Therefore, the number of possible solutions for the inequality is infinity.
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