Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row containi

Question

Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row containing chairs. How many seating arrangements are possible if Akash cannot sit next to Banny and Deol must sit next to Eren?

(A) 288
(B) 240
(C) 144
(D) 120
(E) 96

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Regor60 · Answer

With D and E together as a group and no other restrictions:

ABC F, arranged 5!*2= 240

Subtract from above where A and B are together, as:

C F

The above can be arranged 4!*2*2 ways = 96

Total ways: 240-96= 144

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Can,Will · Answer

gmatophobia  
can you please provide a detailed explanation.
i am not able to understand the role of "and" in question

gmatophobia · Answer

Hi  AnujL

We have 6 members in here - A, B, C, D, E and F

There are two conditions that the solution need to satisfy

1) A cannot sit next to B.

This means any arrangement in which A & B appear next to each other is invalid

Ex. A B C D E F is  NOT  a valid arrangement as A and B appears next to each other.

2) D should sit next to E.

Because its a AND condition, both condition 1 and condition 2 must satisfy.

Let's handle  condition 2  first, Because D and E should always sit next to each other we will take them as single group, say  .

Within  , either E can on the left and D can on the right, or vice versa. So there are 2 ways of arranging the members within  .

We will come to condition 1 a moment later, but say, if that condition weren't there we can arrange A, B, C,   , F in  5! * 2  ways.

Note :   has two members in it. Hence we multiplied by 2

However, in this arrangement A and B can come next to each other. So condition 1 has not been met yet. To fulfil  condition 1  we will subtract those cases in which A and B are together.

As before, we will group A & B into a single group, say  . If we were to arrange  , C,  , F --- it can be done in  4! * 2 * 2  ways.

Note : The multiplication of 2 * 2 is done as we have two groups now, and within each group there are two ways of arranging the members.

So number of ways = (5! * 2) - (4! * 2 * 2)

Taking 4! * 2 as common

= 4! * 2 (5 - 2)

= 4 * 3 * 2 * 2 * 3 = 144 ways.

Hope this clarifies.

bumpbot · Answer

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Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row containi

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