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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
In how many ways can the following diagram be colored, subject to: (i) Each of the smaller triangles is to be painted with one of three colors — red, blue, or green. (ii) No two adjacent regions have the same color.
Solution
The figure has 4 small triangles (1 top, 3 at the base). Let top be colored in 3 ways. The 3 base triangles are adjacent, so they must all be different and also different from the top if adjacent. ⇒ Choose color for top: 3 ways ⇒ Choose 3 distinct colors for bottom row (arranged 3! = 6 ways). ⇒ But bottom middle and top are adjacent → exclude same color combinations. Valid colorings = $3 \times (3! - 3! / 3) = 3 \times 8 = 24.$Online Test Series, Information About Examination,
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