What is the probability of randomly selecting an arrangement of the le

Question

What is the probability of randomly selecting an arrangement of the letters of the word "MEDITERRANEAN" in which the first letter is E and the last letter is R?

A. 1/13
B. 1/20
C. 1/26
D. 1/50
E. 1/100

Bunuel · Accepted Answer

There are 13 letters in MEDITERRANEAN, out of which E appears thrice, N appears twice, A appears twice, and R appears twice.

The number of arrangements of MEDITERRANEAN is therefore  \frac{13!}{3!2!2!2!} .

The number of arrangements in which the first letter is E and the last letter is R is  \frac{11!}{2!2!2!}  (we are left with 11 letters out of which E appears twice, N appears twice and A appears twice).

P = \frac{(\frac{11!}{2!2!2!})}{(\frac{13!}{3!2!2!2!})}=\frac{11!}{2!2!2!}*\frac{3!2!2!2!}{13!}=\frac{3!}{12*13}=\frac{1}{26} .

Answer: C.

TestPrepUnlimited · Answer

There are 13 letters, three E's and two R's.

The probability that the first letter is E is  \frac{3}{13} .

The probability that the last letter is R GIVEN the first letter is E is  \frac{2}{12}  because we confirmed we used up one of the E's already.

Thus the probability of both happening is  \frac{3}{13}*\frac{2}{12} = \frac{1}{26}

Ans: C

ParitoshRawat99 · Answer

Total Number of Ways of arranging 13 letters of MEDITERRANEAN = 13!/3!2!2!2!
The number of ways of arranging 11 letters between E and R, which are fixed at the first and last position respectively = 11!/2!2!2!
Probability = (11!/13!)*3!
= (1/13*12)*6
= (1/26)

MathRevolution · Answer

Word: "MEDITERRANEAN" 
Total letters: 13

Total arrangements:  \frac{13!}{ 2! * 2! * 2! * 3!} = \frac{13! }{ 48 }

Desired arrangements in which the first letter is E and the last letter is R =  \frac{11! }{2! * 2! * 2!} = \frac{11! }{ 8}

Probability:  \frac{\frac{11!}{8}}{{\frac{13!}{48}}} = \frac{11! * 48 }{ 13! * 8} = \frac{6 }{ 13 * 12} = \frac{1}{26}

Answer C

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.

What is the probability of randomly selecting an arrangement of the le

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

What is the probability of randomly selecting an arrangement of the le

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