Question

The total number of ways in which 15 identical apple can be distributed among A, B, C and D such that $A$ and $B$ get at least 1 apple, $C$ get at least 2 apple and $D$ get at least 3 apple, is

• A. ${}^{13}{C}_3$
• B. ${}^{12}{C}_3$
• C. ${}^{11}{C}_3$
• D. ${}^{10}{C}_3$

Answer 1

Answer: (C)

$A+B+C+D=15(A\to 1,B\to 1,C\to 2,D\to 3)$
$A^{\prime }+B^{\prime }+C^{\prime }+D^{\prime }=8$
(Begger's method)
number of ways $={}^{11}{C}_3$.