If necessary consult a list of formulasSolutionAnswer Since

(If necessary, consult a list of formulas.)

Answer:

Since the code has 6 digits so we have 6 places to be filled by any one of 10 digits from 0 to 9.

So that when repititions are not allowed,

The first place of the code can be filled by any one of 0,1,2,...,9 that is we have 10 ways

The second place of the code can be filled by 9 ways ( since one digit is already filled so we exclude that digit)

The third place of the code can be filled by 8 ways ( since two digitss is already filled so that we exclude the two digits)

The fourth place of the code can be filled by 7 ways ( since three digits is already filled so that we exclude the three digits)

The fifth place of the code can be filled by 6 ways ( since four digits is already filled so that we exclude the four digits)

The sixth place of the code can be filled by 5 ways ( since three digits is already filled so that we exclude the five digits)

Thus the total number of codes that contains 6 digits ( none is repeated ) using the digits ( from 0 to 9 ) is

10 x 9 x 8 x 7 x 6 x 5 = 151,200