rhine29388 wrote:
Five kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates?
A.12312
B.22536
C.4320
D.11268
E.45072
OE will be posted after 1 week on 1st april 2016
Hi,
some points on the Q..
1) firstly, it can never be a GMAT Q. You do not expect such complicated and cumbersome calculations in ACTUALS. Also, the wordings are much clearer and crisp in ACTUALS.2) The "the best of them gets at least 4 chocolates" in actuals would mean that there is one specific kid who is the best of them. But when you solve it, it can be any of the four and then only you will get the OA.
3) Although it is not a GMAT Q, and you will be wasting time on it as I wasted 4 to 5 minutes on it due to ambiguous details and then more number of steps, the solution will be found in different cases
SOLUTION
CASE I- FOUR to the winner 4 - 3-1-1a) four can be taken in 3 of one kind and 1 of other kind and these two can be choosen out of three brands in 3C2= 3..
3 for the second can be 2 of one brand and 1 of other OR all three of one brand
4-2-2-1a) same case for 4 choclates
b) 2 can be from one brand OR from two different brands
CASE II- FIVE to the winner5-2-1-1a) again these 5 can be any one of the four and can be from any two brands-4C1*3C2*3!=36
b) 2 for the second can be from same brand or two different brands=3*3!=18
c) 1 each can be in two ways
total= 36*18*2= 1296 ways
CASE III- 6 to the winner6-1-1-1a) again these 6 can be given to any four and from any two brands
4C1*3C2*3!=4*3*3*2=72 ways
For knowledge, one can see the solution and learn, BUT for GMAT just SKIP it _________________