P&C

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Wed Sep 07, 2011 5:11 am

In how many ways can you arrange the alphabets of the word PRIVATE such that no two vowels are together?
1: 720
2: 4320
3: 3600
4: 1440
5: 2500

answer is ddddd.

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Source: Beat The GMAT — Data Sufficiency | Wed Sep 07, 2011 5:11 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Sep 07, 2011 5:16 am

consonants = 4
arrange them = 24 ways.
vowels = 3. arrange them = 6 ways.
also 5 spaces in consonants. pick any 3 . 5C3
24*6*10 =1440

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Thu Sep 08, 2011 8:03 am

Why is it 5c3?

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Thu Sep 08, 2011 8:42 am

The arrangement looks as follows. Where the three vowels can only be fitted in one of the gaps

_P_R_V_T_

Firstly, the 3 vowels can be placed and shuffled in any of the 5 gaps in 5P3=60Ways
The four consonants can be adjusted amongst themselves in 4P4=4!=24 Ways

Total number of ways=24*60=1440 ways Hence D

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