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Let $P_{1} \equiv x + y + z = 6 & P_{2} \equiv x + y + z = 11$ be the two parallel planes. Let three points A, B & C are such that their x, y & z co-ordinates can take only positive integral values, then which of the following is/are CORRECT?

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If point A & origin lies on same side of plane $P_{1},$ then A can take 10 different locations in space

If point B & origin lies on same side of plane $P_{2},$ then B can take 10 different locations in space

If point B & origin lies on same side of plane $P_{2},$ then B can take 119 different locations in space

If point C lies between planes $P_{1} & P_{2},$ then it can take 100 different locations in space

answer is A, D.

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Detailed Solution

(A) Number of location $=^{5} C_{3}$
(B) Number of location $=^{10} C_{3}$
D) Number of location $=^{10} C_{3} -^{6} C_{3}$

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