SATHEE: Permutations And Combinations Question 151

Permutations And Combinations Question 151

Question: The number of ways in which four letters of the word ‘MATHEMATICS’ can be arranged is given by [Kurukshetra CEE 1996; Pb. CET 1995]

Options:

A) 136

B) 192

C) 1680

D) 2454

Show Answer

Answer:

Correct Answer: D

Solution:

Word ?MATHEMATICS? has 2M, 2T, 2A, H, E, I, C, S. Therefore 4 letters can be chosen in the following ways. Case I : 2 alike of one kind and 2 alike of second kind $ i.e. $ , $ ^{3}C_2\Rightarrow $ No. of words $ {{=}^{3}}C_2\frac{4\ !}{2\ !\ 2\ !}=18 $ Case II : 2 alike of one kind and 2 different i.e., $ ^{3}C_1{{\times }^{7}}C_2\Rightarrow $ No.of words $ {{=}^{3}}C_1{{\times }^{7}}C_2\times \frac{4\ !}{2\ !}=756 $ Case III : All are different $ i.e. $ , $ ^{8}C_4\Rightarrow $ No. of words $ {{=}^{8}}C_4\times 4\ !=1680 $ . Hence total number of words are 2454.

BETA

sathee@iitk.ac.in

Media coverage of SATHEE

Play Store

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Permutations And Combinations Question 151

Question: The number of ways in which four letters of the word ‘MATHEMATICS’ can be arranged is given by [Kurukshetra CEE 1996; Pb. CET 1995]

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

Menu