If $a,\ b,\ c \in N,$The anumber of points having position vector $a\widehat{\mathbf{i}} + b\widehat{\mathbf{j}} + c\widehat{\mathbf{k}}$ such that $6 \leq a + b + c \leq 10$, is

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $6 \leq a + b + c \leq 10$
$	herefore\ a + b + c = 6,\ 7,\ 8,\ 9,\ 10$
Here $a \geq 1,b \geq 1,\ c \geq 1$
$	herefore$ Required number of ways
$= \ ^{5}C_{2} +^{6}C_{2} +^{7}C_{2} +^{8}C_{2} +^{9}C_{2}$
$= 110$

Q. If $a,\ b,\ c \in N,$The anumber of points having position vector $a\widehat{\mathbf{i}} + b\widehat{\mathbf{j}} + c\widehat{\mathbf{k}}$ such that $6 \leq a + b + c \leq 10$, is

Explanation

Reviewed by Dr. Abubacker

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