Let A = {(a, b, c) : a, b, c are non-negative integers and a + b + 2c = 22}. Then n(A) is equal to : [2026]

Question

Let A = {(a, b, c) : a, b, c are non-negative integers and a + b + 2c = 22}. Then n(A) is equal to : [2026]

Smart Achievers · Accepted Answer

(3)

Let A = {(a, b, c) : a, b, c are non-negative integers and a + b + 2c = 22}

Put c = 0

a + b = 22 i.e., ${}^{23}C_{1}$

Put c = 1

a + b = 20 i.e., ${}^{21}C_{1}$

Put c = 2

a + b = 18 i.e., ${}^{19}C_{1}$

Put c = 11

a + b = 0 i.e., ${}^{1}C_{1}$

n(A) = ${}^{1}C_{1} + {}^{3}C_{1} + {}^{5}C_{1} + . . . + {}^{23}C_{1}$

$= 1 + 3 + 5 + . . . + 23 = {(12)}^{2} = 144$

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