Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let A denote the event that a 6-digit integer formed by 0,1,2,3,4,5,6 without repetition be divisible by 3. The probability of event A is equal to: Option: 1 <br

Let A denote the event that a 6-digit integer formed by 0,1,2,3,4,5,6 without repetition be divisible by 3. The probability of event A is equal to:
Option: 1 \frac{4}{9}
Option: 2 \frac{9}{56}
Option: 3 \frac{11}{27}
Option: 4 \frac{3}{7}

Answers (1)

best_answer

 

\begin{aligned} &\text {Total cases: }\quad\underline{\color{Blue} {6}} \cdot \underline{\color{Blue}{6}} \cdot \underline{\color{Blue}{5}} \cdot \underline{\color{Blue}{4}} \cdot \underline{\color{Blue}{3}} \cdot \underline{\color{Blue}{2}}\\ &n ( s )=6 \cdot 6 ! \end{aligned}

Favourable cases :

Number divisible by 3 = Sum of digits must be divisible by 3

Case - I

1, 2, 3, 4, 5, 6

Number of ways = 6 !

Case - II

0, 1, 2, 4, 5, 6

Number of ways = 5·5!

Case - III

0, 1, 2, 3, 4, 5

Number of ways = 5·5!

n(favourable) = 6! + 2·5·5! = 5! (6+10)

P =\frac{5 !(6+10)}{6 \cdot 6 !}=\frac{4}{9}

Posted by

Suraj Bhandari

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

'Why are they dying only in Kota': SC grills Rajasthan over surge in student suicides
anam-khan

JEE Main 2025 paper 2 final answer key out; NTA drops 4 questions, 2 from BPlanning
anam-khan

JEE Main 2025 session 2 answer key out for BArch, BPlanning; response sheet on jeemain.nta.nic.in

Latest Question