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In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity A and B respectively. Solve the given statements for the both quantities and choose the correct option. Statement I: In a class of 28 boys and 12 girls, a group of 5 boys and 3 girls is to be sent to represent the class in an exhibition. In how many ways can the teacher select the students? Statement II: In a class of 40 students, 1/4 of which are girls, has to take a group of 12 students on an expedition to Nainital. If there must be at least 3 girls in the group, then find the number of ways in which the selection can be done.

In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity A and B respectively. Solve the given statements for the both quantities and choose the correct option. Statement I: In a class of 28 boys and 12 girls, a group of 5 boys and 3 girls is to be sent to represent the class in an exhibition. In how many ways can the teacher select the students? Statement II: In a class of 40 students, 1/4 of which are girls, has to take a group of 12 students on an expedition to Nainital. If there must be at least 3 girls in the group, then find the number of ways in which the selection can be done. Correct Answer Quantity A < Quantity B

Statement I:

Total no. of boys = 28

⇒ No. of ways of selecting 5 boys = 28C­5 = 28!/(5! × 23!) = 98280

Total no. of girls = 12

⇒ No. of ways of selecting 3 girls = 12C3 = 12!/(3! × 9!) = 220

∴ Total no. of ways of selection = 98280 × 220 = 21621600

∴ Quantity A = 21621600

Statement II:

Total no. of students = 40

⇒ No. of girls = 40 × 1/4 = 10

⇒ No. of boys = 40 – 10 = 30

Since the group must have 3 girls,

⇒ No. of ways of selecting 3 girls = 10C3 = 10!/(3! × 7!) = 120

⇒ No. of students left in the class = 40 – 3 = 37

⇒ No. of ways of selecting other 9 students = 37C9 = 37!/(9! × 28!) = 124403620

∴ Total no. of ways of selections = 124403620 + 120 = 124403740

∴ Quantity B = 124403740

∵ 21621600 < 124403740

∴ Quantity A ˂ Quantity B

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