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)

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