JEE MAIN - Mathematics (2021 - 25th July Morning Shift - No. 19)
There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100 k, then k is equal to _____________.
Answer
238
Explanation
Class $$\matrix{
{{{10}^{th}}} & {{{11}^{th}}} & {{{12}^{th}}} \cr
} $$
Total student $$\matrix{ 5 & 6 & 8 \cr } $$
$$\matrix{ 2 & 3 & 5 \cr } \Rightarrow $$ $${}^5{C_2} \times {}^6{C_3} \times {}^8{C_5}$$
Number of selection $$\matrix{ 2 & 2 & 6 \cr } \Rightarrow {}^5{C_2} \times {}^6{C_2} \times {}^8{C_6}$$
$$\matrix{ 3 & 2 & 5 \cr } \Rightarrow {}^5{C_3} \times {}^6{C_2} \times {}^8{C_5}$$
$$\Rightarrow$$ Total number of ways = 23800
According to question 100 K = 23800
$$\Rightarrow$$ K = 238
Total student $$\matrix{ 5 & 6 & 8 \cr } $$
$$\matrix{ 2 & 3 & 5 \cr } \Rightarrow $$ $${}^5{C_2} \times {}^6{C_3} \times {}^8{C_5}$$
Number of selection $$\matrix{ 2 & 2 & 6 \cr } \Rightarrow {}^5{C_2} \times {}^6{C_2} \times {}^8{C_6}$$
$$\matrix{ 3 & 2 & 5 \cr } \Rightarrow {}^5{C_3} \times {}^6{C_2} \times {}^8{C_5}$$
$$\Rightarrow$$ Total number of ways = 23800
According to question 100 K = 23800
$$\Rightarrow$$ K = 238
Comments (0)
