CAT 2017 Question Paper | Quants Slot 2

CAT Questions

Do Permutation and Combination questions scare you ? Do you get confused on which concept to apply while solving questions of this type ? Its time to get over this fear of yours! Solving CAT previous year paper will help you get an idea about the type of questions asked in the CAT Question Paperand the their difficulty levels so that you adapt your Online CAT Preparation accordingly. 2IIM offers you previous year questions with text and video solutions to ease the process! Here is a question on Permutation and Combinations from CAT 2017 Question Paper Slot 2. Try it now!

Question 29 : In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens? [TITA]

---

---

Video Explanation

---

---

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination

Let us assume Amal gets 1 + x pens and Bimal gets 2 + y pens and Kamal gets 3 + z pens
1 + x + 2 + y + 3 + z = 8
x + y + z = 2 (x , y , z being whole numbers) or
x + (1 + y) + (3 + z )
x + y + z = 8 – 3 = 5 (x , y, z being naturals numbers)
Take 5 ones 1 _ 1 _ 1 _ 1 _ 1 , + symbol should be added in any 2 slots. (There are 4 empty slots)
This is done in ⁴C₂ ways = 6 ways.
Alternative method is to list down the possibilities as done below.

The question is "In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens? [TITA]"

Hence, the answer is 6 ways