In how many ways can the letters of the word DIRECTOR be arranged in the form of words so that the two R's do not come together?
Answers
So, “I,E,O” are the vowels mathematically u will get 3! Ways to arrange the vowels .
Now “D,R,C,T,R” are the remaining alphabets .
Condition is that the vowels should always be together so we can assume the vowels as a single alphabet/unit say “X” (‘X’=’I,E,O’) so now we have a new word.
“D,R,C,T,R,X”
And we have to find the possible arrangements for this word ..
Clearly it is 6! ;
Now we know that the alphabet “X” is actually all the vowels grouped together (I.E.O) and the number of possible arrangements for vowels is 3!
hence the answer “total number of ways to rearrange DIRECTOR with vowels grouped together is” : (Possible arrangements of ‘DRCTRX’) x (Possible arrangements of vowels)
6! x 3!;
Answer:
ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
24x2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x2+25x−47=−8ax2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.