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?  Pick:
A) 392
B) 126
C) 26
D) 9
E) 8
Solution:   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.   Hence, 8 students are divided into groups of 5 and 3 in 8C3 = 56 ways.   Case II:   4 students in the first car and 4 in the second.   So, 8 students are divided into two groups of 4 and 4 in 8C4 = 78 ways.   Therefore, the total number of ways in which 8 students can travel is:   56 +70= 
<gadget id="calculator">56 +70</gadget>
<output>126</output>
126   Answer: Option 126
<result>B</result>
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?