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 words can we make for the PERMUTATIONS word using
[#permalink]
07 Oct 2019, 06:00
07 Oct 2019, 06:00
00:00
Question Stats:
50% (01:27) correct
50% (01:45) wrong based on 8 sessions
Hide Show timer Statistics
How many words can we make for the PERMUTATIONS word using only one vowel, and 2 consonant that the vowel always been in middle?
A) 154
B) 155
C) 156
D) 157
E) 158
A) 154
B) 155
C) 156
D) 157
E) 158
Re: How many words can we make for the PERMUTATIONS word using
[#permalink]
19 Oct 2019, 09:03
19 Oct 2019, 09:03
2
This is a bit tricky.
We have 5 vowels and 7 consonants of which 6 are different.
We can select 2 vowels out of 6 in 6P2 ways, but we must remeber that we should also add the cases where a vowel is between 2 T (TET, TAT, ...). Since the vowels are 5 these cases are 5.
Hence, 5 * 6!/4! + 5 = 5*30 + 5 = 155.
Answer is B.
We have 5 vowels and 7 consonants of which 6 are different.
We can select 2 vowels out of 6 in 6P2 ways, but we must remeber that we should also add the cases where a vowel is between 2 T (TET, TAT, ...). Since the vowels are 5 these cases are 5.
Hence, 5 * 6!/4! + 5 = 5*30 + 5 = 155.
Answer is B.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
How many words can we make for the PERMUTATIONS word using
[#permalink]
19 Oct 2019, 13:49
19 Oct 2019, 13:49
2
huda wrote:
How many words can we make for the PERMUTATIONS word using only one vowel, and 2 consonant that the vowel always been in middle?
A) 154
B) 155
C) 156
D) 157
E) 158
A) 154
B) 155
C) 156
D) 157
E) 158
There are two cases to consider:
case i: the two consonants are different
case ii: the two consonants are the same (i.e., both T's)
case i: the two consonants are different
The 1st letter can be P,R,M,T,N or S. So, we can choose the 1st letter in 6 ways
The 2nd letter can be A,E,I,O or U. So, we can choose the 2nd letter in 5 ways
The 3rd letter can chosen in 5 ways, since the 3rd letter must be DIFFERENT from the 1st letter.
By the Fundamental Counting Principle (FCP), we can complete all 3 steps in (6)(5)(5) ways (= 150 ways)
case ii: the two consonants are the same (i.e., both T's)
The 1st letter must be T. So, we can choose the 1st letter in 1 way
The 2nd letter can be A,E,I,O or U. So, we can choose the 2nd letter in 5 ways
The 3rd letter must be T. So, we can choose the 3rd letter in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 3 steps in (1)(5)(1) ways (= 5 ways)
So, the total number of 3-letter words = 150 + 5 = 155
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
RELATED VIDEO
