Let S be the set of permutations of the sequence 1, 2, 3, 4, 5 for whi

Question

Let S be the set of permutations of the sequence 1, 2, 3, 4, 5 for which the first term is not 1. A permutation is chosen randomly from S. The probability that the second term is 2, in lowest terms, is a/b. What is a + b?

(A) 5
(B) 6
(C) 11
(D) 16
(E) 19

Show Answer

Official Answer

E

(A) 5
(B) 6
(C) 11
(D) 16
(E) 19

EgmatQuantExpert · Answer

Solution 
  Given:  
 • S denotes the set of permutations of the sequence 1, 2, 3, 4, 5 for which the first term is not 1.
• A permutation is chosen randomly from S.
• The probability that the second term is 2, in lowest terms, is a/b.

To find:  
 • The value of a + b.

Approach and Working:  
As the first term is not 1, 
 • Total number of ways the first term can be chosen = 4
• And, the number of possible permutations for each of the first terms = 4!
• Hence, total permutations = 4 x 4!

If the second term is 2,
 • Total number of ways the first term can be chosen = 3
• And, the number of possible permutations = 3!
• Hence, total permutations = 3 x 3!

So, the value of a/b = (3 * 3!)/(4 * 4!) = 18/96 = 3/16
 • The value of a + b = 3 + 16 = 19

Hence, the correct answer is option E.

Answer: E

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-AT-e1533292152363.png

Archit3110 · Answer

EgmatQuantExpert 
Could you please explain on why you have done 
So, the value of a/b = (3 * 3!)/(4 * 4!) = 18/96 = 3/16
 • The value of a + b = 3 + 16 = 19

EgmatQuantExpert · Answer

Hey  Archit3110 ,
in the question, a/b is defined as the probability of choosing a set with second term 2.

Now, number of ways we can select a set with second term 2 = 3 * 3!
And, total number of ways we can select a set = 4 * 4!
 Hence, the probability =  \frac{a}{b} = \frac{3 * 3!}{4 * 4!}

In lowest term, the value of the fraction becomes  \frac{3}{16} 
 Hence, a + b = 3 + 16 = 19

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Let S be the set of permutations of the sequence 1, 2, 3, 4, 5 for whi

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

Let S be the set of permutations of the sequence 1, 2, 3, 4, 5 for whi

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