Permutation Numbers arrangement

1.     How many four digits numbers can be formed with digits 1,2,3,4?

Solution:

There are 24 number can be formed of 4 digit number

4

3

2

1

   = 4x3x2x1

   = 24

2.         How many numbers can be formed with digits 1,2,3,4 without repetition?

Solution:

Case 1: there are 4 number of 1 digit.

4

3

Case 2: there are 12 numbers of 2 digits.

4

3

2

Case 3: there are 24 numbers of 3 digits.

4

3

2

1

Case 4: there are 24 numbers of 4 digits.

Hence total required numbers are = 4+12+24+24=64

3.     How many four digit numbers can be formed with the digits 0,1,2,3,4,5 if

i)               Repetition of digits is allowed?

ii)             Repetition of digits is not allowed?

Solution:

Repetition allowed

5

6

6

6

  = 5x6x6x6 =1080      since at thousands place zero can not be placed

            Repetition not allowed

5

5

4

3

                        = 5x5x4x3 = 300

Zero cannot be placed at the thousand place , if it placed 4 digit number reduced to 3 digits.