1. Tardigrade
  2. Question
  3. Mathematics
  4. All possible 5 lettered words are formed using all the letters of the word COCOA and a word from it is randomly selected. The chance that any two alike letters are not adjacent in the selected word, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. All possible 5 lettered words are formed using all the letters of the word "COCOA" and a word from it is randomly selected. The chance that any two alike letters are not adjacent in the selected word, is

Probability - Part 2

Solution:

$ n(S)=\frac{5 !}{2 ! 2 !}=30$
$E$ : required event
$n ( E )=30-( n ( A \cup B ))$
where $n(A)$ is number of words when C's togather etc.
image
$n(A \cup B)=n(A)+n(B)-n(A \cap B) $
$=\left(\frac{4 !}{2 !}\right)+\frac{4 !}{2 !}-3 !=24-6=18=12$
image
$P(E)=\frac{12}{30}=\frac{2}{5} $