(Q). A class contains 4 boys and x girls. In a test only 5 students including at least 3 boys can appear. If different group of students appear for the exam every time, if the number of times test conducted is 435 then find the total number of students in the class.
Solution:-
B G
4 x
Number of ways to select 5 student is
3B2G + 4B1G
= ⁴C₃ × ˣC₂ + ⁴C₄ × ˣC₁
= + 1 × x
= 2x² – x
this is same as the number of test conducted which is 435
∴ 2x² – x = 435
2x² – x -435 = 0
2x²- 30x + 29x – 435 = 0
2x(x-15) + 29(x-15) = 0
(x-15)(2x+29) = 0
∴ x = 15 = number of girls in class
Hence total number of student in class
= 4 + 15
= 19 Answer