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

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)

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

Thanks!

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