Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Probability
0 votes

If the letters of the word ASSASSINATION are arranged at random.Find the probability that no two A's are coming together

$\begin{array}{1 1}(A)\;\large\frac{15}{26}\\(B)\;\large\frac{5}{26}\\(C)\;\large\frac{25}{26}\\(D)\;\large\frac{9}{26}\end{array} $

Can you answer this question?

1 Answer

0 votes
Given the word : ASSASSINATION
No two A's are coming together
ASSASSINATION can be arranged in $\large\frac{13!}{3!\times 4!\times 2!\times 2!}$ ways
No two A's coming together XSXSXSXSXIXNXTXIXOXNX
A can be put in place of any X.It can be put in 11 places in $11C_3$ ways
Number of favorable conditions =$\large\frac{10!}{(4!\times 2!\times 2!\times 11C_3)}$
Step 2:
$\therefore$ Probability =$\large\frac{\Large\frac{10!}{(4!\times 2!\times 2!\times 11C_3)}}{\Large\frac{13!}{(3!\times 4!\times 2!\times 2!)}}$
$\Rightarrow \large\frac{15}{26}$
Hence (A) is the correct answer.
answered Jul 8, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App