Latest iGate Aptitude Question SOLUTION: in how many ways can the letters of the word college be arranged.such that its vowels do not come to gether

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(#M40037222) IGATE Numerical Ability question permutation and combination Keep an EYE

in how many ways can the letters of the word college be arranged.such that its vowels do not come to gether

Asked In iGate (10 years ago)

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Varunraj Reddy  (10 years ago)

Total no.of words COLLEGE can be arranged in 7!/2!*2!=1260
Vowels OEE come together=CLLG(OEE)=5!/2!*3!/2!=60*3=180
Vowels do not come together=1260-180=1080

Is this solution Helpfull? Yes (34) | No (3)  

manjulavani  (10 years ago)

college=7!/2!*2!=1260
5!/2!*3!/2!=180
1260-180=1080

Is this solution Helpfull? Yes (8) | No   

gnaneswar singh  (8 years ago)

COLLEGE is a 7 letter word.
here E and L will appears two times so we will get in denominator (2!*2!)
COLLEGE can be arranged in 7!/(1!*1!*2!*2!*1!)=1260
It is difficult to calculate Vowels don't come together now we are going to calculate vowels come together.
CLLG(OEE) =4+1 consider OEE as one letteer.
then vowels come together =(5!/2!)*(3!/2!)=180 (3!/2! is the arrangement of vowels total 3 vowels 3! and E repeats two times.)
vowels don't come together =1260-180=1080.

Is this solution Helpfull? Yes (6) | No   

Vishal Chugh  (10 years ago)

The ans should be 1080.
It can be calculated as:
Total possible combinations from word College = 7!/(2!*2!)=1260
Combinations in which vowels appear together = (5!/2!)*(3!/2!)=180
So combinations in which vowels don't appear together = 1260 - 180 = 1080

Is this solution Helpfull? Yes (5) | No (1)  

NIKHIL RANAJN  (8 years ago)

1080 IS THE ANS

Is this solution Helpfull? Yes (1) | No (1)  

chandravadan chourasia  (8 years ago)

7!/2!*2!=1260
5!/2!*3!/2!=180
1260-180=1080

Is this solution Helpfull? Yes (1) | No   

sidhartha kumar  (8 years ago)

COLLEGE:-
we will arrange this one in:-
7!/2!*2!=1260.
1) vowels come together:- (o,e,e)
we arrange (o,e,e) in 3!/2! ways.
and we take (o,e,e) as 1 word. and now total we have 5!/2!*2!.
now we will multiply
3!/2!*2! * 5!/2!*2!=90.
2) vowels do not come together:-
1260-90 = 1170.

Is this solution Helpfull? Yes (1) | No (4)  

PURBASHA ROY  (8 years ago)

Here you are considering only the words where the vowels o,e,e together. But we have to consider those words also where only 2 of the 3 vowels are together.
So, here we are taking 4 consonants.
c,l,l,g.
These are to be written like _c_l_l_g_
These 4 consonants can be selected in 4!/2! ways.
Then 3 vowels can be places in 5 positions in 5P3/2! ways
So the no. of words where vowels are together is=4!/2! * 5P3/2! =360
so the no of words where vowels are not together=1260-360 =900

Is this solution Helpfull? Yes | No (5)  

Manish  (8 years ago)

college can be formed in 7!/2!*2!=1260
Vowels OEE come together=CLLG(OEE)=5!/2!*3!/2!=60*3=180
remaining 1260-180=1080

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Madhusudhana  (8 years ago)

4p3*4p3*2
=1152

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