Permutation and Combination  Quant/Math  CAT 2016
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)
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 ^{8}C_{3} ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in ^{8}C_{4} ways.
Therefore, the total number of ways in which 8 students can travel is ^{8}C_{3} + ^{8}C_{4} = 56 + 70 = 126.
XLRI XAT TANCET Practice Question Samples
Sorted by Subject
Algebra,
Arithmetic & Geometric Progressions,
Averages and Mean,
Clocks and Calendars,
Data Sufficiency,
English Grammar,
Function,
Geometry,
Coordinate Geometry,
Mensuration,
Trigonometry,
Interest,
Inequality,
Mixtures & Alligations,
Number System and Theory,
Percentages,
Profit & Loss,
Permutation & Combination,
Probability,
Ratio, Proportion,
Set Language and Theory,
Speed, Time & Distance,
Races,
Pipes & Cisterns And Work & Time,
Miscellaneous,
General Knowledge.


Quick Links
Staying outside India? 

Ascent offers CAT Correspondence Course for those who reside abroad.


GMAT Math eBook Series 

GMAT Math eBooks series on high scoring topics such as permutation combination, number theory, geometry. US$ 6.99.


