How many words can be formed using all the letters of "EQUAT

Question

How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:

Bunuel · Accepted Answer

Responding to a pm. Since there are 8 distinct letters in the word EQUATION, then the # of arrangements of these letters would be 8!. Now, in half of these cases A will be after Q and in half of these cases Q will be after A. Therefore the final answer is \frac{8!}{2}=\frac{7!*8}{2}=4*7! . Answer: C. Questions about the same concept to practice: six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html in-how-many-different-ways-can-the-letters-a-a-b-91460.html mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html Hope it helps.

gmatdog · Answer

Answer C.

There are 8 unique alphabets, so 8! ways of arranging them.

For the restriction of A coming after Q -
Among all possible arrangements, in half of the cases A will be before Q - and in the other half it will be after Q.

So answer = 8! / 2 = 8 / 2 x 7! = 4 x 7!

cyberjadugar · Answer

Hi, These are some awesomely worded questions. :-D

Regards,

sanjoo · Answer

how can we knw that there will be half times A will cum after Q and Q after A???

m confused ..!!

Bunuel · Answer

Ask yourself: why should any of these two orderings have preferences over the other. Does probability favor one ordering over another?

Follow the links in my previous posts to practice more questions about this concept.

Hope it helps.

sach24x7 · Answer

Are there any restrictions while using this approach? Can you please explain?

cyberjadugar · Answer

Hi,

The only restriction that you should keep in mind is that how the arrangements are made. In this question, sequence of two alphabets is mentioned. Further extrapolation can be made for three alphabets. For E comes after Q, and Q comes after U, required cases would be 1/6 of total arrangements.
E,Q and U can be arranged in 3! or 6 ways. While the sequence EQU in that order will occur only once.

Hope it helps.

Regards,

mvictor · Answer

I will never forget the lesson on combinatorics presented by  mikemcgarry  on Magoosh. 
so..we have 8 different letters. these can be arranged in 8! ways.
for every possible way when A comes after Q, there is a combination when A comes before Q. so we need to divide by 2.

8!/2 = 8*7!/2 => 4*7!

bumpbot · Answer

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How many words can be formed using all the letters of "EQUAT

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How many words can be formed using all the letters of "EQUAT

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