How many 3 letter words (meaningful or meaningless) can be formed using letters from the word INTELLECTUAL? A) 336 B) 3

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 24, 2020 4:46 am

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How many 3 letter words (meaningful or meaningless) can be formed using letters from the word INTELLECTUAL?

A) 336
B) 370
C) 399
D) 400
E) None of these

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Last edited by GMATinsight on Fri Jul 24, 2020 4:48 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Fri Jul 24, 2020 4:46 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

Re: How many 3 letter words (meaningful or meaningless) can be formed using letters from the word INTELLECTUAL? A) 336

by GMATinsight » Fri Jul 24, 2020 4:47 am

GMATinsight wrote:How many 3 letter words (meaningful or meaningless) can be formed using letters from the word INTELLECTUAL?

A) 336
B) 370
C) 399
D) 400
E) None of these

[textarea]www.GMATinsight.com[/textarea]

Frequency of letters
I - 1
N - 1
T - 2
E - 2
L - 3
C - 1
U - 1
A - 1

3 letter words

Case 1: All letters identical (LLL)
1 ways

Case 2: Two letters identical and third different (LLA)
3*7*3 = 63 ways

Case 3: All letters distinct (INT)
8C3*3! = 56*6 = 336 ways

Total = 1+63+336 = 400

Answer: Option D

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