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24 Jun 2023, 05:39
Kudos
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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:
20% (03:11) correct
80%
(03:08)
wrong
based on 45
sessions
History
Date
Time
Result
Not Attempted Yet
How many different 5-letter groups can be selected from the letters of the word "CANADIANS"?
A. 21
B. 36
C. 37
D. 41
E. 42
A. 21
B. 36
C. 37
D. 41
E. 42
24 Jun 2023, 07:07
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Bunuel
C AAA NN D I S
Case 1: The selected letter group doesn't have any repeating alphabets
- Number of ways of selecting 5 alphabets out of 6 alphabtes = \(^6C_5\)
Total number of ways = 6
Case 2: The selected letter group has exactly two repeating alphabets
- The two repeating alphabets can be either 'A' or 'N'. The number of ways of selecting A or N = \(^2C_1\)
- The remaining three alphabets can be selected in \(^5C_3 \) ways
Total number of ways = 2 * 10 = 20
Case 3: The selected letter group has exactly three repeating alphabets
- The repeating alphabet can only be A. The number of ways of selecting A = \(1\)
- The remaining two alphabets can be selected in \(^5C_2 \) ways
Total number of ways = 10 * 1 = 10
Case 4: The selected letter group has two pairs of repeating alphabets and one non-repeating alphabet
- The two repeating alphabets can only be A and N. We need to select both. The number of ways of selecting A and N= \(1\)
- The remaining alphabet can be selected in \(^4C_1 \) ways
Total number of ways = 4 * 1 = 4
Case 5: The selected letter group has only repeating alphabets
- The repeating alphabets can only be A and N. We need to select both. The number of ways of selecting A and N= \(1\)
Total number of ways =1
Total:
Sum of each cases = 6 + 20 + 10 + 14 + 1 = 41
IMO Option D
07 Sep 2024, 05:29
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