Help please!

The probability is 7/9.

My guess:

Total number of arrangements of  0, 1, 6,  and  7   =   4!   =   24

For each of these, there are 2 possible choices for the first three digits.

So the total number of possibilities  =  24 * 2   =   48

Only one of these 48 possibilities is correct, so the probability that Fatima chooses the correct one is

1 / 48

----------(below is my reassurance that there are actually 24 ways to arrange the last 4 digits!)----------

0167

0176

0617

0671

0716

0761

1067

1076

1607

1670

1706

1760

6017

6071

6107

6170

6701

6710

7016

7061

7106

7160

7601

7610

thank you for all the help!

hectictar had the correct answer :)