how many combinations could we have if this restriction was not imposed? find that and then subtract the number of four repeated digits there can be (there are only 10: 0,0,0,0; 1,1,1,1; 2,2,2,2; 3,3,3,3; etc)

i assume repetitions are allowed, since you didn't say they weren't.2) Over the years, the state of California has used different combinations of letter of the alphabet and digits on its automobile license plates.

a. At one time license plates were issued that consisted of three letters followed by three digits. How many different license plates can be issued under this arrangement?

we choose 3 letters and 3 digits. there are 26 letters and 10 digits (including 0).

so for the first letter we have 26 choices.

for each of those choices, we have 26 choices for the 2nd letter

for each of those choices, we have 26 choices for the 3rd letter

for each of those choices, we have 10 choices for the 1st digit

for each of those choices, we have 10 choices for the 2nd digit

for each of those choices, we have 10 choices for the 3rd digit

so in all, we have 26*26*26*10*10*10 choices

do this in the way i did the aboveb. Later on, license plates were issued that consisted of three digits followed by three letters. How many different license plates can be issued under this arrangement?

maybe it's just me, or there is something missing from the question. is there a minimum grade we are hoping the student will get? how many penalties is the student allowed? ...3) An exam consists of ten true-or-false questions. In how many ways may the exam be completed if a penalty is imposed for each incorrect answer, so that a student may leave questions unanswered?