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 (integer)
238
Solution
Class $\matrix{
{{{10}^{th}}} & {{{11}^{th}}} & {{{12}^{th}}} \cr
}$<br><br>Total student $\matrix{
5 & 6 & 8 \cr
}$<br><br>$\matrix{
2 & 3 & 5 \cr
} \Rightarrow$ ${}^5{C_2} \times {}^6{C_3} \times {}^8{C_5}$<br><br>Number of selection $$\matrix{
2 & 2 & 6 \cr
} \Rightarrow {}^5{C_2} \times {}^6{C_2} \times {}^8{C_6}$$<br><br>$$\matrix{
3 & 2 & 5 \cr
} \Rightarrow {}^5{C_3} \times {}^6{C_2} \times {}^8{C_5}$$<br><br>$\Rightarrow$ Total number of ways = 23800<br><br>According to question 100 K = 23800<br><br>$\Rightarrow$ K = 238
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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