Problem Solving

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter).

a. 4
b. 5
c. 6
d. 12
e. 24

answer is B

Thank you for you help.

Order does not matter so its a combination problem.

Plugin and solve.

Since we are asked for the minimum value start with 4

We can choose 1 color from 4 colors in 4c1 ways
No of combinations possible for choosing 2 colors from 4 colors is 4c2

4c1 + 4c2(=10) is less than 12 so not sufficient
5c1+5c2 > 12 so this will be the answer

Hence B.

Regards,
CR

CRAMYA IS ALIVE!!!

480ocean wrote:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter).

a. 4
b. 5
c. 6
d. 12
e. 24

answer is B

Thank you for you help.

The answer can not be 12 or 24 because just using only one of these numbers is more than enough so it is either 4,5 or 6

4 needs 8
5 needs 7
6 needs 6

for C(X:2)

4 gives us only 6 - NOT ENOUGH
5 gives us 10 - ENOUGH!

Thanks for your help! I didn't quite understand the books explanation.