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Statement-1: The number of non-negative ...

Statement-1: The number of non-negative integral solutions of `x+y+z=40" is """^(43)C_(3)`.
Statement-2: The number of ways of distributing n identical items among r persons giving zero or more items to a person 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 provided in the question regarding the number of non-negative integral solutions and the distribution of identical items. ### Step 1: Analyze Statement 1 We need to find the number of non-negative integral solutions for the equation: \[ x + y + z = 40 \] This is a classic problem in combinatorics, and we can use the "stars and bars" theorem to solve it. According to the theorem, the number of non-negative integral solutions of the equation \( x_1 + x_2 + ... + x_r = n \) is given by: \[ \binom{n + r - 1}{r - 1} \] ...
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