Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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Question 4 the day: May 20, 2003

The question for the day is from the topic Permutation and Combination.

Question:

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?

(1) 9
(2) 26
(3) 126
(4) 3920

Correct Answer - (3)

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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

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 in ⁸C₃ ways.

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in ⁸C₄ ways.

Therefore, the total number of ways in which 8 students can travel is ⁸C₃ + ⁸C₄ = 56 + 70 = 126.