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04 Dec 2022, 11:31
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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:
38% (02:25) correct
62%
(02:47)
wrong
based on 74
sessions
History
Date
Time
Result
Not Attempted Yet
How many different 4-letter groups can be selected out of the letters of the word TENNESSEE, if the order of the letters in the groups does not matter ?
A. 14
B. 15
C. 16
D. 17
E. 18
A. 14
B. 15
C. 16
D. 17
E. 18
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04 Dec 2022, 12:18
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Bunuel
As the order of the letters does not matter, we need to focus only on selection of the letters.
T
N N
S S
E E E E
We require four letter words.
Case 1: No repetition
There are four distinct alphabets. The alphabets can we selected in 4C4 ways = 1.
Total : 1 way
Case 2: One repeating pair
The repeating pair can be selected from three available alphabets (E, N and S) .
As we need only one alphabet from the available three repeating alphabets, the selection can be done in 3C1 = 3 ways
Once we have have selected the repeating pair, we need two distinct alphabets from the three available 3 alphabets.
This selection can be done in 3C2 = 3 ways.
Total : 3 * 3 = 9 ways
Case 3: Two repeating Pairs
Two alphabets that repeat can be selected from three available alphabets (E, N and S) .
We need only two alphabet from the available three repeating alphabets, the selection can be done in 3C2 = 3 ways
Total : 3 ways
Case 4: Three Alphabets repeat
The only possible alphabet that can repeat thrice is E.
We still need the fourth distinct alphabet, which can be selected from the three available alphabets in 3C1 ways.
Total : 1 * 3 = 3 ways
Case 5: Four Alphabets repeat
The only possible alphabet that can repeat four times is E.
Total : 1 way
Sum = 1 + 9 + 3 + 3 + 1 = 17 ways
Option D
General Discussion
