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mohan514
On how many ways can the letters of the word "COMPUTER" be arranged?

1}Vowels occupy the even positions.
i mean what are the possibile arrangements???

I think it's meant that vowels can occupy only even positions:

C|O|M|P|U|T|E|R
O|E|O|E|O|E|O|E (O and E stand for odd and even positions respectively).

# of arrangements would be \(C^3_4*3!*5!=4!*5!=2880\).

\(C^3_4\) - choosing which 3 even positions out of 4 will be occupied by vowels (there are 4 even positions: 2nd, 4th, 6th and 8th and only 3 vowels);
\(3!\) - # of different arrangements of these vowels on their even positions;
\(5!\) - # of different arrangements of 8-3=5 other letters left.

Hope it helps.

hi man

I am getting 5 even positions
please help me out

| C | M | P | T | R |
O E O E O E O E O E O

separating the consonants, I have inserted the vowels into the gaps

what is wrong here, please do say to me, man

thanks in advance
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Bunuel
mohan514
On how many ways can the letters of the word "COMPUTER" be arranged?

1}Vowels occupy the even positions.
i mean what are the possibile arrangements???

I think it's meant that vowels can occupy only even positions:

C|O|M|P|U|T|E|R
O|E|O|E|O|E|O|E (O and E stand for odd and even positions respectively).

# of arrangements would be \(C^3_4*3!*5!=4!*5!=2880\).

\(C^3_4\) - choosing which 3 even positions out of 4 will be occupied by vowels (there are 4 even positions: 2nd, 4th, 6th and 8th and only 3 vowels);
\(3!\) - # of different arrangements of these vowels on their even positions;
\(5!\) - # of different arrangements of 8-3=5 other letters left.

Hope it helps.

hi man

I am getting 5 even positions
please help me out

| C | M | P | T | R |
O E O E O E O E O E O

separating the consonants, I have inserted the vowels into the gaps

what is wrong here, please do say to me, man

thanks in advance

There are 8 letters in "COMPUTER" there are 4 even positions: 1st-2nd-3rd-4th-5th-6th-7th-8th
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In how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?

A. 480
B. 576
C. 720
D. 960
E. 2880

COMPUTER
Vowels = OUE ; can be positioned in 4c3 *3! ways = 24
and others 5! ways ; 120
so total 120*24 ; 2880
IMO E
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Bunuel

In GMAT exam, if we ran into similar questions but with larger factorials , how to calculate the factorials of a large number quickly within 2 minute time frame?

While solving a similar question, i ran into a bigger number such as this 10C4∗2!∗4!∗7!2!=25,401,600. I took longer time to reach the solution. Is there a shortcut or simpler steps to get final answer without involving larger multiplications ?

Thanks much
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jakolik
In how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?

A. 480
B. 576
C. 720
D. 960
E. 2880
Solution:

We see that the word “COMPUTER” has 8 letters and 3 vowels: O, U and E. Since there are 4 even positions (i.e, 2nd, 4th, 6th and 8th positions) and order matters, the 3 vowels can occupy the 4 even positions in 4P3 = 4 x 3 x 2 = 24 ways, and the 5 consonants can occupy the remaining positions (not occupied by a vowel) in 5! = 120 ways. Therefore, there are a total of 24 x 120 = 2880 ways to arrange the letters in the word “COMPUTER” if the vowels occupy the even positions.

Answer: E
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