Question

Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner.
Further,
1. 2 and 3 are not to immediately follow each other
2. 1 is not to be immediately followed by 3
3. 4 is not to appear at the last place
4. 1 is not to appear at the first place
How many different numbers can be formed ?
(a) 6
(b) 8
(c) 9
(d) None of the above​

Answer 1

Answer:

Step-by-step explanation:

the number is _ _ _ _

the first _ cannot be 1

so let's try for 2.

2 _ _ _

the second _ cannot be 3. last _ cannot be 4 so 4 must come either 2nd or 3rd _.

2 4 _ _

Now 3 cannot follow 1 so it has to be: 2413.

2 _ 4 _ has to  be 2143.

Id the first _ was 3 then:

3 _ _ _

the second _ cannot be 2. last _ cannot be 4 so 4 must come either 2nd or 3rd _.

3 4 _ _

Now it can be any one- 3412 or 3421.

3 _ 4 _

it can't be 2 after 3 so, it's 3142

If 4 was the first _ then:

4 _ _ _

combinations (2,3,1) ; (3,2,1) ; (2,1,3) are ruled out.

it can be: 4312.

In total we have 6