Question

The number of ways in which 8 non-identical applies can be distributed among 3 boys such that every boy should get atleast 1 apple & atmost 4 apples is K.${}^7{P}_3$ where K has the value equal to :

• A. $88$
• B. $66$
• C. $44$
• D. $22$

Answer 1

The correct option is A $88$

Case (a) $(4,3,1)$

Number of ways

$3!{\times }^8{C}_4{\times }^4{C}_3=6\times 70\times 4=1680$

Case (b) $(4,2,2)$

Number of ways

$3{\times }^8{C}_4{\times }^4{C}_2=3\times 70\times 6=1260$

Case (c) $(2,3,3)$

Number of ways

$3{\times }^8{C}_2{\times }^6{C}_3=3\times 28\times 20=1680$

Hence total number of possibilities $=4620$