Question

Assertion :If $a,b,c$ are positive integers such that $a+b+c\le 8$ , then the number of possible values of the ordered triplets $(a,b,c)$ is $56$. Reason: The number of ways in which n distinct things can be distributed among $r$ girls such that each get at least one is ${}^{n-1}{C}_n$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Consider $a+b+c\le 8$
The number of possible ordered triplets is
$={}^8{P}_{(3-1)}$
$={}^8{P}_2$
$=\frac{8!}{6!}$
$=56$.
Consider the reason,
Now ${}^{n-1}{C}_n$ is not possible as $n-1<n$ and $(-n)!$ is not defined for any natural number n.
For ${}^n{C}_r$ $n\ge r$ and $n,r\ge 0$
Hence the reason is false.