A Team Of 8 Students Goes On An Excursion, In Two Cars, Of Which One

1.	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?
Answer» 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 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: 8C3+8C4=56+70= 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 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: 8C3+8C4=56+70= 126.

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?

Answer»

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

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:

8C3+8C4=56+70= 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

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:

8C3+8C4=56+70= 126.