The number plates consists of 3 letters of the English alphabet follow

Question

The number plates consists of 3 letters of the English alphabet followed by 3 digits. What is the probability that a randomly picked number plate contain 3 same letters followed by 3 same digits ?

A. 1/260
B. 1/33,800
C. 1/43,200
D. 1/67,600
E. 1/135.200

ZIX · Accepted Answer

The probability of all alphabets same:

\frac{26}{26}*\frac{1}{26}*\frac{1}{26}

The first alphabet can be any letter so the probability is  \frac{26}{26} = 1 . For the second letter to be the same as first, the probability is  \frac{1}{26} , similarly for third letter to be same too, we multiply again by  \frac{1}{26} .

For digits:

\frac{10}{10}*\frac{1}{10}*\frac{1}{10}

Same logic as above. We have 10 total choices for 0-9 digits.

Now multiply both together to find probability of all of these events occurring together:

(\frac{26}{26}*\frac{1}{26}*\frac{1}{26})(\frac{10}{10}*\frac{1}{10}*\frac{1}{10}) = \frac{1}{67600}

Kinshook · Answer

Given: The number plates consists of 3 letters of the English alphabet followed by 3 digits. 
Asked: What is the probability that a randomly picked number plate contain 3 same letters followed by 3 same digits ?

Total number of ways for choosing the number plate = 26^3*10^3 = 17576000
Favorable number of ways for choosing the same number plate = 1
Probability = 1/17576000

A. 1/260
B. 1/33,800
C. 1/43,200
D. 1/67,600
E. 1/135.200

Bunuel 
Please check what is the mistake in the above solution.

firas92 · Answer

Number of ways of making a number plate with 3 same letters followed by 3 same digits=26*1*1*10*1*1

So probability of picking a number plate containing 3 same letters followed by 3 same digits = (26*1*1*10*1*1)/(26*26*26*10*10*10)=1/67600

Posted from my mobile device

luisdicampo · Answer

Deconstructing the Question  
Structure of the plate:   followed by  .
Total Letters available = 26.
Total Digits available = 10.

Condition: "3 same letters" AND "3 same digits".

Step 1: Total Possible Outcomes  
Since repetition is allowed (implied for license plates):
- Ways to choose 3 letters =  26 	imes 26 	imes 26 = 26^3 
- Ways to choose 3 digits =  10 	imes 10 	imes 10 = 10^3 
Total Outcomes =  26^3 	imes 10^3 .

Step 2: Favorable Outcomes  
- Ways to have 3 same letters (AAA, BBB... ZZZ) =  26 .
- Ways to have 3 same digits (000, 111... 999) =  10 .
Favorable Outcomes =  26 	imes 10 .

Step 3: Calculate Probability  
 P = \frac{	ext{Favorable}}{	ext{Total}} 
 P = \frac{26 	imes 10}{26^3 	imes 10^3}

Simplify by canceling one 26 and one 10:
 P = \frac{1}{26^2 	imes 10^2} 
 P = \frac{1}{676 	imes 100} 
 P = \frac{1}{67600}

Answer:  D

shivani1351 · Answer

The number plates consists of 3 letters of the English alphabet followed by 3 digits. What is the probability that a randomly picked number plate contain 3 same letters followed by 3 same digits ?

The correct option should be Option D. 1/67,600, and here's why:

Let any such number plate be visually represented as A1 A2 A3 D1 D2 D3 (where A1, A2, A3 represent 3 letters of the English aphabet and D1, D2, D3 represent the 3 digits present in the number plate).

We are required to find out the probability that a number plate contains A A A D D D (A represents the same letter and D represents the same digit)

Now, the total ways of forming such number plates = 26C1*1*1*10C1*1*1
 Reasoning:  The common letter can be selected in a total of 26C1 or 26 ways, this selected letter would be present at the 2nd and 3rd positions as well, hence there's only 1 way to select the 2nd 3rd alphabet. Now, for selecting the digits, the common digit can be selected in a total of 10C1 or 10 ways. This selected digit would present at the 5th and the 6th positions as well, hence we're left with only 1 way to select the 5th and 6th digits.

The overall total number of ways of forming the number plates without any constraint = 26C1*26C1*26C1*10C1*10C1*10C1 = 26*26*26*10*10*10

Therefore, required probability = (26*10)/(26*26*26*10*10*10) = 1/67,600

Hence, option (D) is the correct answer.

The number plates consists of 3 letters of the English alphabet follow

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The number plates consists of 3 letters of the English alphabet follow

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards