BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Que: A color “code” is defined as a sequence of three dots arranged in a row....

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Que: A color “code” is defined as a sequence of three dots arranged in a row....

by Max@Math Revolution » Sat Dec 05, 2020 10:58 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Que: A color “code” is defined as a sequence of three dots arranged in a row. Each dot is colored either “red” or “black.” How many distinct codes can be formed?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 1
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: Que: A color “code” is defined as a sequence of three dots arranged in a row....

by Max@Math Revolution » Tue Dec 08, 2020 8:40 am
Solution: Number of ways arranging ‘n’ objects out of which ‘r’ objects are identical is n!/ r!

Case I: Let us assume we use two BLACK and 1 RED dot. Thus, the total way of arranging them is 3!/2! = 3

Case II: Similarly, let us assume we use two RED and 1 BLACK dot. Thus, the total way of arranging them is 3!/2! = 3

Case III: All three BLACK: 3!/3! = 1

Case IV: All three RED: 3!/3! = 1

Total number of codes: 3 + 3 + 1 + 1 = 8

The first dot can use RED or BLACK, the second dot also can use RED or BLACK, and the third dot also can do, so 2*2*2=8

Therefore, D is the correct answer.

Answer D
Top
Post new topic Post Reply
• Page 1 of 1