Hard counting problem p2 (from Kaplan Qbank)

GRE Quant Problem Solving
1

Hey all!

Can anyone explain me how to get to the right answer in this problem? Thanks!!!

The 8 items A, B, C, D, E, F, G and H are to be displayed on a shelf on a straight line. In how many different ways can the items be displayed if item B is to be placed to the right item of A, and item C is to be placed to the right of item B?

a) 120
b) 560
c) 3,600
d) 5,040
e) 6,720

2

Does it mean immediate right, or right in general?
The answer would be different in both cases.
I am going to assume it means right in general, because “immediate” is not mentioned anywhere.

The total ways in which we can arrange these 8 letters = 8!
The total ways in which we can arrange the letters A,B,C = 3! = 6
Of the 6 total ways in which we can arrange A, B, C; only 1 will satisfy the condition given in the equation, (ie item B is to be placed to the right item of A, and item C is to be placed to the right of item B)
This means only 1/6 of the total arrangements of the 8 letters will satisfy this condition.
Answer = 1/6 * 8! = 6720 (E)

3

Awesome! Pretty intuitive now that you explain it like this.

Thanks!

4

The 8 items A, B, C, D, E, F, G, and H are to be displayed on a straight line. In how many ways can the items be displayed if item B must be placed in any position that is to the right of item A, and item C must be placed in any position that is to the right of B?

A 120

B 560

C 3600

D 5040

E 6720

5