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# How many different 3-letter words can be formed from the word “ZINNIA”

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Joined: 04 Jan 2015
Posts: 2432
How many different 3-letter words can be formed from the word “ZINNIA”  [#permalink]

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Updated on: 13 Aug 2018, 05:29
00:00

Difficulty:

95% (hard)

Question Stats:

32% (01:59) correct 68% (02:35) wrong based on 77 sessions

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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
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

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Originally posted by EgmatQuantExpert on 18 Apr 2018, 04:26.
Last edited by EgmatQuantExpert on 13 Aug 2018, 05:29, edited 3 times in total.
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Re: How many different 3-letter words can be formed from the word “ZINNIA”  [#permalink]

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Updated on: 23 Apr 2018, 03:48

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 Z or,
o Two I.
• = Ways to select 1 group of similar letters from 2 groups * ways to different from remaining 3-different letters * arranging all three letters

• = $$^2C_1$$ * $$^3C_1$$*$$\frac{3!}{2!}$$
• =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.

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Originally posted by EgmatQuantExpert on 18 Apr 2018, 04:31.
Last edited by EgmatQuantExpert on 23 Apr 2018, 03:48, edited 1 time in total.
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Joined: 30 Mar 2017
Posts: 134
GMAT 1: 200 Q1 V1
Re: How many different 3-letter words can be formed from the word “ZINNIA”  [#permalink]

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18 Apr 2018, 19:09
1
1
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

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Re: How many different 3-letter words can be formed from the word “ZINNIA”  [#permalink]

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23 Apr 2018, 03:58
Hey Everyone,

Official solution to the question has been posted.

Regards,
Ashutosh
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Re: How many different 3-letter words can be formed from the word “ZINNIA” &nbs [#permalink] 23 Apr 2018, 03:58
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