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Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity A∶ In how many different ways can the letters of the word PAINTER be arranged in such a way that the vowels occupy only the even positions? Quantity B∶ There are 12 points in a plane out of which 4 are collinear. Find the number of lines that can be formed from 12 points.

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity A∶ In how many different ways can the letters of the word PAINTER be arranged in such a way that the vowels occupy only the even positions? Quantity B∶ There are 12 points in a plane out of which 4 are collinear. Find the number of lines that can be formed from 12 points. Correct Answer Quantity A > Quantity B

Quantity A∶

Since vowels E, A and I will occupy 3 even positions, then consonants P, N, T and R will be placed at 4 odd position;

Then the positions of vowels and consonants will be same but they can be shuffled.

No. of ways to arrange these letters such that vowel occupy even places only = 3! × 4! = 144

Quantity B∶

From 12 points, number of lines formed = 12C2

Since 4 points are collinear, number of lines formed by these = 4C2

∴ Total lines = 12C2 – 4C2 + 1 = 66 – 6 + 1 = 61

∴ Quantity A > Quantity B

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