In how many ways can the fruit be laid out?

Question

An apple, an orange, a strawberry, a nectarine and a pear are laid out in a straight line. The orange is not at either end and is somewhere to the left of the pear.

Answer 1

For this we assume that there are 5 places in which we have to arrange these fruits.we will find out choices for each place.

I am going to use letters A,O,S,N and P

As orange cant be at the ends places and pear cant be arranged at the first and second place as then orange will be at right of the pear .we will discuss all the cases and find out the possible arrangements for each case.

 

So if orange is at second place : total choices=3*3*2*1=18

choices for first place:3

third place :3

fourth place:2

fifth place :1

 

if orange is at third place:total choices =3*2*2*1=12

choices for first place:3
second place:2 (as we cant arrange pear in a position so that orange will be at left )
fourth place:2
fifth place :1

 

If orange is at fourth place:total choices=3*2*1*1=6

choices for first place:3

second place:2(again for the same reason pear cant be arranged to this place)

third place:1(for the same reason pear again cant be arranged to this place also)

fourth place:1

 

Total no. of ways of arrangement=18+12+6=36