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A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

Correct Answer: 126

Explanation:

There are 8 students and the maximum capacity of the cars together is 9.


 


We may divide the 8 students as follows


 


Case I: 5 students in the first car and 3 in the second Or


 


Case II: 4 students in the first car and 4 in the second


 


Hence,     in Case I: 8 students are divided into groups of 5 and 3 in  8 C 3  ways.


 


Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in  8 C 4  ways.


 


Therefore, the total number of ways in which 8 students can travel is


 


8 C 3 + 8 C 4  = 56 + 70 = 126.


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