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

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and theother only 4. In how many ways can they travel? Correct Answer 126

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 8C3 ways.

 

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4 ways.

 

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

 

8C3+8C4 = 56 + 70 = 126.

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