CAT 2021 Question Paper | Quant Slot 2

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 1 : The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

Video Explanation

Explanatory Answer

Given that, there are 15 identical balloons, 6 identical pencils, and 3 identical erasers.
We need to distribute these items among 3 children, such that each child gets at least four balloons and one pencil.
So, every person gets four balloons and one pencil. After distribution, we have 3 balloons, 3 pencils, and 3 erasers remaining.
So, let’s first arrange the balloons in all possible combinations.
(3, 0, 0) , (2, 1, 0) , (1, 1, 1)
We can arrange (3, 0, 0) in three ways.
We can arrange (2, 1, 0) in six ways.
We can arrange (1, 1, 1) in only one way.
So, we can arrange balloons among three children in 10 ways.
Likewise, we can also arrange 3 pencils in 10 ways and 3 erasers in 10 ways.
Therefore, the total number of ways is 10 x 10 x 10 = 1000 ways

The question is " The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is "

Hence, the answer is '1000'