Latest Patni Aptitude Question SOLUTION: In how many ways the word ENGINEERING can be arranged so that no vowel come together???

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In how many ways the word ENGINEERING can be arranged so that no vowel come together???

Asked In Patni praveena (11 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

Saraswathy  (11 years ago)

Total no. of ways ENGINEERING can be arranged is
E=3, N=3, G=2, I=2, R=1
=> 11!/(3!*3!*2!*2!) => 277200

No. of ways vowels come together
Vowels ==> (eieei)ngnrng =>
eieei can be considered as 1 letter ... so 1!
ngnrng = 6!
eieei can be arranged as 5!/(3!*2!)
ngnrng can be arranged as 6!/(3!*2!)

So (1!+6 !)*5!/(3!*2!*3!*2!)
=> 4200

So no. of ways vowels not come together
=> 277200 - 4200 = 273000

Ans : 273000

Is this solution Helpfull? Yes (18) | No (4)  

Ann Theressa  (11 years ago)

1800

ENGINEERING==>E=3, N=3, G=2, I=2, R=1

ie there are 5 vowels and 6 consonants.Since no vowels should come together the possible combinations are,
1)
C V C V C V C V C V C

2)
C C V C V C V C V C V

3)
V C V C V C V C V C C

Where V represents vowel and C consonant.

(1) combination can be arranged in = 6!/(3!*2!) *5!/(3!*2!) = 600 ways

Similarly (2) and (3) combinations can be arranged in 600 ways each.

Total no. of ways letters can be arranged so that no vowel come together
= 600+600+600
=1800 ways

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Dilip sharma  (10 years ago)

6!*5!
=720*120
=86400

Is this solution Helpfull? Yes | No (1)  

Dilip sharma  (10 years ago)

ENGINEERING==>E=3, N=3, G=2, I=2, R=1

ie there are 5 vowels and 6 consonants.Since no vowels should come together the possible combinations are,
1)
C V C V C V C V C V C

2)
C C V C V C V C V C V

3)
V C V C V C V C V C C

Where V represents vowel and C consonant.

C can be arranged =6! = 720
V can be arranged =5! = 120
for three conditions 120*3= 360
therefor word ENGINEERING can be arranged so that no vowel come together = 720*360
= 259200

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