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05 Sep 2022, 11:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:18) correct
57%
(02:20)
wrong
based on 140
sessions
History
Date
Time
Result
Not Attempted Yet
How many four-letter words can be formed using the letter of the word ‘HARVARD’?
A. 120
B. 192
C. 198
D. 270
E. 276
A. 120
B. 192
C. 198
D. 270
E. 276
08 Sep 2022, 04:18
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A typical question where we should create scenarios.
The word is HARVARD
So the answer = 120 + 144 + 6 = 270
Option. D
The word is HARVARD
- The number of letters: H, V, D - 1 each and A, R - 2 each
- Scenario 1:All the letters are distinct.
- Since we have a total of 5 distinct letters so we can directly use the filling space method to get the possible number of ways \(=5 \times 4 \times 3 \times 2 \times 1 = 120\) ways
Scenario 2: Two letters are identical and two letters are distinct.
- The two identical letters can be either A or R so we have 2 choices.
Next, we can select the remainder of two distinct letters from the 4 remaining letters (Do note, that if we chose R and R as identical letters then now we can select one A so we have H, V, D, and A all available.
So this gives us \(4C2 = 6\) ways
So now we have a case which would be HDRR (just one example) type. We can arrange them in \(\frac{4!}{2!} = 12 \) ways
So total ways = \(2 \times 6 \times 12 = 144\) ways
- Scenario 2: Two sets of two identical letters (AABB type)
- We can clearly do that by selecting AARR and they can be arranged in \(\frac{4!}{2! \times 2!}\) = 6 ways
So the answer = 120 + 144 + 6 = 270
Option. D
16 Apr 2024, 13:40
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Hi Bunuel, are there any similar questions like this one within GMAT Club that I can practice? I have already solved this one on an official practice exam: https://gmatclub.com/forum/how-many-3-l ... 21859.html and would like more practice if possible with these kinds of problems, where we need to break the outcomes into various cases.
