Arithmetic Ability
Permutations and Combinations

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Q.

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?

View Answer

Correct choice: A

Explanation:

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
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