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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?
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 = 126
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 = 126