In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?
a) 1,008
b) 1,296
c) 1,512
d) 2,016
e) 2,268
I have tried first to get the totals by grouping ABC and FGH as one unit so that I can have 4 elements to be 4!=24
Then, I have found the number of times DE can be which is 2!=2
ABC= 3!=6 and FGH=3!=6 Why the answer cannot be 24*6*6*2 =1728 that is not the right answer provided.
Why do I have to try to do it as a combination like the following
8!/ (2!)(6!) = 28
Then that value 28 multiplied with the options ABC, FGH, and DE = 28*2*6*6 will give me the right answer 2,010.
Could someone tell me what is that I don't have correct on my original concept?
Thanks in advance
a) 1,008
b) 1,296
c) 1,512
d) 2,016
e) 2,268
I have tried first to get the totals by grouping ABC and FGH as one unit so that I can have 4 elements to be 4!=24
Then, I have found the number of times DE can be which is 2!=2
ABC= 3!=6 and FGH=3!=6 Why the answer cannot be 24*6*6*2 =1728 that is not the right answer provided.
Why do I have to try to do it as a combination like the following
8!/ (2!)(6!) = 28
Then that value 28 multiplied with the options ABC, FGH, and DE = 28*2*6*6 will give me the right answer 2,010.
Could someone tell me what is that I don't have correct on my original concept?
Thanks in advance
