JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(A=\{(a,b,c): a,b,c \text{ are non-negative integers and } a+b+2c=22\}\). Then \(n(A)\) is equal to:
- A \(121\)
- B \(124\)
- C \(144\)
- D \(169\)
Answer & Solution
Correct Answer
(C) \(144\)
Step-by-step Solution
Detailed explanation
The given equation is \(a + b + 2c = 22\), where \(a, b, c\) are non-negative integers. This can be rewritten as \(a + b = 22 - 2c\). Since \(a \ge 0\) and \(b \ge 0\), we must have \(22 - 2c \ge 0\), which gives \(c \le 11\). Since \(c\) is a non-negative integer, the possible…
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