GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
How many different four-letter words can be formed (the wor
[#permalink]
14 May 2019, 00:05
14 May 2019, 00:05
Expert Reply
1
Bookmarks
00:00
Question Stats:
48% (01:59) correct
51% (01:40) wrong based on 45 sessions
Hide Show timer Statistics
How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R?
(A) \(8P_2\)
(B) \(\frac{8P_2}{2!*2!}\)
(C) \(8P_4\)
(D) \(\frac{8P_4}{2!*2!}\)
(E) \(\frac{10P_2}{2!*2!}\)
(A) \(8P_2\)
(B) \(\frac{8P_2}{2!*2!}\)
(C) \(8P_4\)
(D) \(\frac{8P_4}{2!*2!}\)
(E) \(\frac{10P_2}{2!*2!}\)
Re: How many different four-letter words can be formed (the wor
[#permalink]
10 Feb 2020, 19:30
10 Feb 2020, 19:30
1
Carcass wrote:
How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R?
(A) \(8P_2\)
(B) \(\frac{8P_2}{2!*2!}\)
(C) \(8P_4\)
(D) \(\frac{8P_4}{2!*2!}\)
(E) \(\frac{10P_2}{2!*2!}\)
(A) \(8P_2\)
(B) \(\frac{8P_2}{2!*2!}\)
(C) \(8P_4\)
(D) \(\frac{8P_4}{2!*2!}\)
(E) \(\frac{10P_2}{2!*2!}\)
Place one G in the first slot and one R in the last slot:
G __ __ R
The remaining letters, {G, R, E, A, I, O, U, S}, can be arranged in the remaining 2 slots in \(8P_2\) [no indistinguishable(same) objects nor repetition]. The answer is (A).
Note: Since the two G’s in the base word are indistinguishable, the word G 1 G 2 AR is the same as G 2 G 1 AR. Hence, the internal arrangement of the G’s or, for the same reason, the R’s is not important.
Re: How many different four-letter words can be formed (the wor
[#permalink]
18 Aug 2020, 11:03
18 Aug 2020, 11:03
Can you please explain how they are not important?
To me, G1 G2 R1 R2 are the same, so we would get repetition with GGRR, GRGR, GG_R, and G_RR
To me, G1 G2 R1 R2 are the same, so we would get repetition with GGRR, GRGR, GG_R, and G_RR
