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Statement-1: The number solutions of the...

Statement-1: The number solutions of the equations x+y+z=15 in the set N of all natural numbers is `""^(14)C_(2)`.
Statement-2: The number of ways of distributing n identical items among r persons is `""^(n+r-1)C_(r-1)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

AI Generated Solution

To solve the problem, we need to analyze both statements and determine their validity step by step. ### Step-by-Step Solution **Step 1: Analyze Statement 1** We need to find the number of solutions to the equation \( x + y + z = 15 \) where \( x, y, z \) are natural numbers (i.e., \( x, y, z \in \mathbb{N} \)). Since \( x, y, z \) are natural numbers, the minimum value for each of them is 1. Thus, we can redefine the variables: ...
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