Question

Assertion :There are 4 addressed envelopes & 4 letters for each of them. The probability that no letter mailed in its correct envelope is $\frac{3}{8}$ Reason: The probability that all letters are not mailed correctly is $\frac{23}{24}$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is B Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion

$n\left(S\right)=4!=24$
Now number of ways in which all letters go to correct envelope is only one way.
$\therefore$ The probability that all letters are correctly placed in
right envelope $=\frac{1}{24}$
$\therefore$ The probability that all letters are not correctly placed
in right envelope $=1-\frac{1}{24}=\frac{23}{24}$
$\therefore$ Reason (R) is correct
Again the, probability that out of $n$ letters & $n$ envelopes none of them enter in the right envelop.
$=(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}+...+\frac{(-1{)}^n}{n!}),n\ge 2usingn=4$
$P$(None of the letter go to the exact envelop)$=\frac{1}{2}-\frac{1}{6}+\frac{1}{24}$
$=\frac{12-4+1}{24}=\frac{9}{24}=\frac{3}{8}$
$\therefore$ Assertion (A) is also correct but Reason (R) is not the proper explanation of the Assertion (A).