Find the number of students in section C, of class VII if a group of 4

1.	Find the number of students in section C, of class VII if a group of 4 students has formed from the class VII in such a way that one student from each section(A, B and C) and the remaining students from any of the section and number of students in section A and B are 16 and 24.The number of ways to form a 4students group is 437760.1. 102. 143. 204. 155. 18
Answer» Correct Answer - Option 3 : 20 Given Number of students in section A = 16 Number of students in section B = 24 Calculation: Let the number of students in section C is x One student is from each student, so remaining one student is selected from the remaining students such that (16 + 24 + x – 3) = 37 + x ⇒¹⁶C₁ × ²⁴C₁ × ^xC₁ × ^{37 + X}C₁ = 437760 ⇒ 16 × 24 × X × (37 + X) × (36 + X)!/(36 + X)! = 437760 ⇒ X(37 + X) = 1140 ⇒ X² + 37X – 1140 = 0 using discriminant method: D = b² -4ac = (37)² – 4(1)(-1140) = 5929 X = (-b + √D)/2a = -(37 + 77 )/2 = 20 ∴ The number of students is 20.

Find the number of students in section C, of class VII if a group of 4 students has formed from the class VII in such a way that one student from each section(A, B and C) and the remaining students from any of the section and number of students in section A and B are 16 and 24.The number of ways to form a 4students group is 437760.1. 102. 143. 204. 155. 18

Answer» Correct Answer - Option 3 : 20

Given

Number of students in section A = 16

Number of students in section B = 24

Calculation:

Let the number of students in section C is x

One student is from each student, so remaining one student is selected from the remaining students such that (16 + 24 + x – 3) = 37 + x

⇒¹⁶C₁ × ²⁴C₁ × ^xC₁ × ^{37 + X}C₁ = 437760

⇒ 16 × 24 × X × (37 + X) × (36 + X)!/(36 + X)! = 437760

⇒ X(37 + X) = 1140

⇒ X² + 37X – 1140 = 0

using discriminant method:

D = b² -4ac

= (37)² – 4(1)(-1140)

= 5929

X = (-b + √D)/2a

= -(37 + 77 )/2

= 20

∴ The number of students is 20.