# total number of combinations

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• Sep 11th 2007, 11:26 AM
xojuicy00xo
total number of combinations
Hey. I have 3 problems I can't get. If anyone can help with how to do any of them, it would be appreciated.

1) To gain access to his account, a customer using an ATM must enter a four-digit code. If repetition of the same four digits is not allowed (for example, 5555) how many possible combinations are there?

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?
b. 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?

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?
• Sep 11th 2007, 11:53 AM
Jhevon
Quote:

Originally Posted by xojuicy00xo
Hey. I have 3 problems I can't get. If anyone can help with how to do any of them, it would be appreciated.

1) To gain access to his account, a customer using an ATM must enter a four-digit code. If repetition of the same four digits is not allowed (for example, 5555) how many possible combinations are there?

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)

Quote:

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?
i assume repetitions are allowed, since you didn't say they weren't.

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

Quote:

b. 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?
do this in the way i did the above

Quote:

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?
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? ...
• Sep 11th 2007, 04:47 PM
Soroban
Hello, xojuicy00xo!

Quote:

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?

For each of the ten questions, the student has three choices:
. . (1) answer "True", (2) answer "False", (3) skip it.

There are: .\$\displaystyle 3^{10} \:=\:59,049\$ ways.

• Sep 11th 2007, 04:49 PM
Jhevon
Quote:

Originally Posted by Soroban
Hello, xojuicy00xo!

For each of the ten questions, the student has three choices:
. . (1) answer "True", (2) answer "False", (3) skip it.

There are: .\$\displaystyle 3^{10} \:=\:59,049\$ ways.

i'm not the type to skip questions, even when incorrect answers carry a penalty, so i wouldn't even think of this third choice:o