There are 720 permutations of the digits 1, 2, 3, 4, 5, 6. Suppose these permutations are arranged from smallest to largest numerical values, beginning from 1 2 3 4 5 6 and ending with 6 5 4 3 2 1 Then the digit in unit place of number at 267Tth position is ________ .

Number of numbers beginning with $1=120$                                                                  

1

Number of numbers beginning with $2=120$                                                                 

2

Starting with 31 ………………………………$=24$

3

1

Starting with 3214 …………………………….$=2$

3

2

1

4

Finally                                                              $= 1$
                                                                              

3

2

1

5

4

6

                                                               
Hence, unit place digit of 267th number is 6.