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Updated on: 13 Aug 2018, 06:29
Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:26.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:29, edited 3 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:29, edited 3 times in total.
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C
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:
46% (02:24) correct
54%
(02:18)
wrong
based on 354
sessions
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Time
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Not Attempted Yet
3 Deadly mistakes in Permutation and Combination - Exercise Question #4
4- How many different 3-letter words can be formed from the word “ZINNIA”?
Options
Learn to use the Keyword Approach in Solving PnC question from the following article:
Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions
Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
Article-3: 3 deadly mistakes you must avoid in Permutation & Combination
4- How many different 3-letter words can be formed from the word “ZINNIA”?
Options
- A. 12
B. 34
C. 42
D. 62
E. 94
Learn to use the Keyword Approach in Solving PnC question from the following article:
Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions
Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
Article-3: 3 deadly mistakes you must avoid in Permutation & Combination
Updated on: 29 Apr 2023, 01:35
Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:31.
Last edited by Bunuel on 29 Apr 2023, 01:35, edited 2 times in total.
Last edited by Bunuel on 29 Apr 2023, 01:35, edited 2 times in total.
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Solution
Given:
• We are given a 6-letter word- ‘ZINNIA’.
To find:
• We need to find the number of 3-letter different words using the letters of ‘ZINNIA’.
Approach and Working:
ZINNIA is a letter word having two N, two I, one Z, and one A.
Thus, different three letter words can be formed in two ways:
- • Using 2 same and 1 different Or,
• Using all different letters.
- o Using Z, I, and A.
3-letter words using 2 same and 1 different letters:
- • We have 2 groups of similar letters
- o Two N or,
o Two I.
- • = \(^2C_1\) * \(^3C_1\)*\(\frac{3!}{2!}\)
• =2*3*6*/2=18
3-letter words using all different letters:
- • We have 4 different letters – Z, I, N, A.
• Thus, ways to form 3-letter word from 4 different letters=\(^4P_3\)=24
Thus, Total three letter words= 18+24=42.
Hence, the correct answer is option C.
Answer: C
General Discussion
18 Apr 2018, 20:09
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Number of different 3 letter words = (# of 3 letter words with two Is) + (# of 3 letter words with two Ns) + (# of 3 letter words with every letter distinct)
# of 3 letter words with two Is: (# of ways to select two Is) * (# of ways to select a 3rd letter) * (# of ways to place that 3rd letter)
# of ways to select two Is = 1
# of ways to select a 3rd letter = 3 (select 1 letter from Z,N,A)
# of ways to place that 3rd letter = 3 (*I*I* --> * marks where we can place the 3rd letter)
# of 3 letter words with two Is = 1*3*3 = 9
# of 3 letter words with two Ns = 9 (same logic as above)
# of 3 letter words with every letter distinct: (# of ways to arrange 3 out of the 4 distinct letters) = 4P3 = 24
Number of different 3 letter words = 9+9+24=42
Answer: C
# of 3 letter words with two Is: (# of ways to select two Is) * (# of ways to select a 3rd letter) * (# of ways to place that 3rd letter)
# of ways to select two Is = 1
# of ways to select a 3rd letter = 3 (select 1 letter from Z,N,A)
# of ways to place that 3rd letter = 3 (*I*I* --> * marks where we can place the 3rd letter)
# of 3 letter words with two Is = 1*3*3 = 9
# of 3 letter words with two Ns = 9 (same logic as above)
# of 3 letter words with every letter distinct: (# of ways to arrange 3 out of the 4 distinct letters) = 4P3 = 24
Number of different 3 letter words = 9+9+24=42
Answer: C
