Answer:
the total number of arrangement is six
Explanation:
Part (a) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other.
Suppose A and B are together and form a group, then no. of groups are .
These groups can be arranged in
A and B can be arranged in .
Therefore, the possible no. of arrangements are .
Part (b) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B.
Total no. of arrangements with six letters
The no. of arrangements in which A is before B
Therefore, the possible no. of arrangements are .
Part (c) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and B is before C.
Total no. of arrangements with six letters
A, B and C can be arranged in
Out of these 6 arrangements, there is only one arrangement in which A is before B and B is before C.
So, the possible no. of ways =
Therefore, the possible no. of arrangements are .
Part (d) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and C is before D.
The no. of arrangements in which A is before B
Out of these arrangements, half will be with C before D and half will be with D before C.
Therefore, the possible no. of arrangements are .
Part (e) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other and C and D are also next to each other.
If A and B form one group and C and D from another group then there are groups and these groups can be arranged in
A and B can be arranged in
Similarly, C and D can be arranged in
Therefore, the possible no. of arrangements are .
Part (f) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that E is not last in line.
The no. of arrangements in which the position of E is fixed at last
The no. of arrangements in which the position of E is not fixed
Therefore, the possible no. of arrangements are