DEV Community

Cover image for "Day 48 of My Learning Journey: Setting Sail into Data Excellence! ⛵️ Today's Focus: Maths for Data Analysis ( Per & Com - 3)
Nitin-bhatt46
Nitin-bhatt46

Posted on

"Day 48 of My Learning Journey: Setting Sail into Data Excellence! ⛵️ Today's Focus: Maths for Data Analysis ( Per & Com - 3)

#data #dataengineering #datascience #maths

PERMUTATION AND COMBINATION - 3

NUMERICAL

Four visitors A,B,C & D arrive at a town which has 5 hotels. In how many ways can they disperse themselves among 5 hotels, if 4 hotels are used to accommodate them.

Ans. A has 5 possibility
B has 4 possibility
C has 3 possibility
D has 2 possibility

Now we have the possibility but everything has to be done simultaneously so,
Multiplication rule will be used.

TOTAL POSSIBILITY ARE = 5*4*3*2 = 120

In how many ways can 5 letters be mailed if there are 3 mailboxes available if each letter can be mail in any mailbox.

   Ans. letter 1  has 3 possibility
Enter fullscreen mode Exit fullscreen mode

letter 2 has 3 possibility
letter 3 has 3 possibility
letter 4 has 3 possibility
letter 5 has 3 possibility

    Everything has to be done simultaneously 
    So, 3*3*3*3*3 = 243
Enter fullscreen mode Exit fullscreen mode

Every telephone number consists of 7 digits. How many telephone numbers are there which do not include any other digits but 2,3,5 & 7 ?

   Ans.  Digit 1 has 4 possibility
Enter fullscreen mode Exit fullscreen mode

Digit 2 has 4 possibility
Digit 3 has 4 possibility
Digit 4 has 4 possibility
Digit 5 has 4 possibility
Digit 6 has 4 possibility
Digit 7 has 4 possibility

    Everything has to be done simultaneously 
    So, 4^7.
Enter fullscreen mode Exit fullscreen mode

Find the number of 5 lettered palindromes which can be formed using the letter from the english alphabet ?

   Ans.  The total alphabet is 26.
Enter fullscreen mode Exit fullscreen mode

Letter 1 has 26 possibility
Letter 2 has 26 possibility
Letter 3 has 26 possibility
Letter 4 has 1 possibility
Letter 5 has 1 possibility

    Everything has to be done simultaneously 

    So, 26*26*26*1*1 = 26^3.
Enter fullscreen mode Exit fullscreen mode

How many 10 digit numbers can be made with an odd digit so that no two consecutive digits are the same ?

   Ans.  The consecutive digits must not be the same.

    Odd number 1,3,5,7,9.
Enter fullscreen mode Exit fullscreen mode

Digit 1 has 5 possibility
Digit 2 has 4 possibility
Digit 3 has 4 possibility
Digit 4 has 4 possibility
Digit 5 has 4 possibility
Digit 6 has 4 possibility
Digit 7 has 4 possibility
Digit 8 has 4 possibility
Digit 9 has 4 possibility
Digit 10 has 4 possibility

    Everything has to be done simultaneously 

    So, 5* 4^9.
Enter fullscreen mode Exit fullscreen mode

🙏 Thank you all for your time and support! 🙏
Don't forget to catch me daily at 6:30 Pm (Monday to Friday)for the latest updates on my programming journey! Let's continue to learn, grow, and inspire together! 💻✨

Top comments (0)

Read next

aashwinkumar profile image

CountVectorizer vs TfidfVectorizer

Ashwin Kumar -

mikeyoung44 profile image

AI-Powered Code Completion: Faster, Smarter, and Fully Local Editing for IntelliJ IDEs

Mike Young -

mikeyoung44 profile image

Selective Attention Boosts Transformer Performance on Language Tasks

Mike Young -

mikeyoung44 profile image

Frontier AI Developers Need Internal Audit Function to Address Key Governance Challenges

Mike Young -