A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?  Choices
A) 110 B) 123 C) 126 D) 154 E) 165
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 in8C3 ways.   Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.   Therefore, the total number of ways in which 8 students can travel is:   \inline {\color{Blue}8126_{3}+8126_{4}}=56 + 70= 
<gadget id="calculator">56 + 70</gadget>
<output>126</output>
126   126
<result>C</result>
A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?