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Find the number of integral solutions of equation
x + y + z + t = 29, x > 0 , y > l , z> 2 and t > 0.
- a)27C3
- b)28C3
- c)2600
- d)29C4
Correct answer is option 'C'. Can you explain this answer?
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Find the number of integral solutions of equationx + y + z + t = 29, x...
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Find the number of integral solutions of equationx + y + z + t = 29, x...
In the solution, why haven't we added 1 to t, given that t is also greater than 0?
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Find the number of integral solutions of equationx + y + z + t = 29, x...
We can start by listing out all possible factorizations of 29 into four positive integers:
29 x 1 x 1 x 1
1 x 29 x 1 x 1
1 x 1 x 29 x 1
1 x 1 x 1 x 29
For each factorization, we can find the number of ways to assign the factors to x, y, z, and t. For example, for the first factorization, x can be 29, y can be 1, z can be 1, and t can be 1, or x can be 1, y can be 29, z can be 1, and t can be 1, and so on. There are 4 ways to assign the factors to x, y, z, and t for each factorization.
Therefore, the total number of integral solutions is:
4 x 4 = 16
29 x 1 x 1 x 1
1 x 29 x 1 x 1
1 x 1 x 29 x 1
1 x 1 x 1 x 29
For each factorization, we can find the number of ways to assign the factors to x, y, z, and t. For example, for the first factorization, x can be 29, y can be 1, z can be 1, and t can be 1, or x can be 1, y can be 29, z can be 1, and t can be 1, and so on. There are 4 ways to assign the factors to x, y, z, and t for each factorization.
Therefore, the total number of integral solutions is:
4 x 4 = 16
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Find the number of integral solutions of equationx + y + z + t = 29, x > 0 , y > l , z> 2 and t > 0.a)27C3b)28C3c)2600d)29C4Correct answer is option 'C'. Can you explain this answer?
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