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Given below are two quantities named A & 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 between the possible answers. Quantity A: Find the number of words that can be formed from the word ‘CONVENIENCE’ so that the words start with 2 E’s and end with 2 N’s. Quantity B: A committee of 7 students is to be formed out of 8 students from class 12th and 6 students from class 11th. In how many ways can this committee be formed if in the committee, majority of 12th class students is required?

Given below are two quantities named A & 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 between the possible answers. Quantity A: Find the number of words that can be formed from the word ‘CONVENIENCE’ so that the words start with 2 E’s and end with 2 N’s. Quantity B: A committee of 7 students is to be formed out of 8 students from class 12th and 6 students from class 11th. In how many ways can this committee be formed if in the committee, majority of 12th class students is required? Correct Answer Quantity A > Quantity B

Quantity A:

‘CONVENIENCE’

It has 11 words: 3 N’s, 3 E’s, 2 O’s, I, C and V

If the words start with 2 E’s and end with 2 N’s, that means First two and last two positions are fixed.

Now remaining 7 positions must be filled with N, E, 2 O’s, I, C and V;

∴ Number of words = 7!/2! = 5040/2 = 2520

Quantity B:

A committee of 7 students is to be formed out of 8 students from class 12th and 6 students from class 11th;

Since we want majority of 12th class students:

Possible combinations: 4(12th class) and 3(11th class) + 5(12th class) and 2(11th class) + 6(12th class) and 1(11th class) + 7(12th class)

∴ Number of ways to form the committee = 8C4 × 6C3 + 8C5 × 6C2 + 8C6 × 6C1 + 8C7

⇒ 70 × 20 + 56 × 15 + 28 × 6 + 8

⇒ 1400 + 840 + 168 + 8

⇒ 2416

∴ Quantity A > Quantity B

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