A licence plate consists of seven symbols: digits or letters. How many license plates are there...

A licence plate consists of seven symbols: digits or letters. How many license plates are there if the following is true:

(a) there must be three letters and four digits, and symbols may repeat?

(b) no restrictions on the quantity of letters and numbers, and symbols may repeat?

Solutions

Expert Solution

a) Here we require seven symbols on the number plate.

Given that number plate contains three letter and four digits. We know that there 10 digits and 26 letter or alphabets. We have to choose any 4 numbers from 10 and 3 alphabets from 26. And symbols may repetative.

Hence required number of plates are as follows :

. Thus totally 175760000 number plates can be made.

b) Here no restrictions on choosing the symbols for creating seven symbols number plate. And repetation also allowed here.

Hence we can choose the combinations of 2 whose addition is 7.

i.e. (1,6),(2,5),(3,4),(4,3),(5,2),(6,1). We have to choose both digits and letters simultaneously hence 0 can not be contain.

Hence the total number of number plates are as follows:

Thus total numbers of plates are 5003631360.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A licence plate consists of seven symbols: digits or letters. How many licence plates are there...

A licence plate consists of seven symbols: digits or letters. How many licence plates are there if the following is true: (1) there must be three letters and four digits, and symbols may repeat? (2) no restrictions on the quantity of letters and numbers, and symbols may repeat?

An automobile license plate consists of 3 letters followed by 4 digits. How many different plates...

An automobile license plate consists of 3 letters followed by 4 digits. How many different plates can be made: a. If repetitions are allowed? b. If repetitions are not allowed in the letters but are allowed in the digits? c. If repetitions are allowed in the letters but not in the digits?

How many possible license plates can be manufactured if a license plate consists of three letters...

How many possible license plates can be manufactured if a license plate consists of three letters followed by three digits and (a) the digits must be distinct, the letters can be arbitrary? (b) the letters must be distinct; the digits can be arbitrary? (c) The digits and the letters must be distinct.

If a license plate consists of two letters followed by four digits, how many different licenses...

If a license plate consists of two letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated.

A swedish license plate consists of three letters followed by three digits. Find the probability that...

A swedish license plate consists of three letters followed by three digits. Find the probability that a randomly selected plate has a) no duplicate letters b) no duplicate digits c) all letters the same d) only odd digits e) no duplicate letters and all digits equal

1) A set of license plates has four letters followed by 4 digits. (a) In how...

1) A set of license plates has four letters followed by 4 digits. (a) In how many ways can a license plate be made with four letters followed by 4 digits? (Letters or digits may be repeated.) (b) In how many ways can a license plate be made with four different letters followed by 4 different digits? (c) If a license plate is made with four letters followed by 4 digits, what is the probability that it has no repeated...

1)How many license plates are there if they start with three capital letters followed by 4...

1)How many license plates are there if they start with three capital letters followed by 4 digits from 0 to 9. (Note that letters and digits can be repeated? 2)In how many ways can 5 men and 5 women be arranged in a line if the line starts with a man, and the men and women alternate?

A license plate in a certain state consists of 4 digits, not necessarily distinct, and 3...

A license plate in a certain state consists of 4 digits, not necessarily distinct, and 3 letters, also not necessarily distinct. (a) How many distinct license plates are possible if no restriction? (b) How many distinct license plates are possible if it must begin and terminate by a digit? (c) How many distinct license plates are possible if it must begin and terminate by a letter? (d) How many distinct license plates are possible if the three letters must appear...

License plates in a given state must consist of three letters followed by four digits. The state's...

License plates in a given state must consist of three letters followed by four digits. The state's DMV has determined that there are eighteen three-letter words that cannot appear on license plates, and there are five four-digit numbers that cannot appear. How many license plates are banned? Your answer may be given as an integer, or as a formula. Either is acceptable.

How many: New York license plates can be made that consist of 3 letters followed by...

How many: New York license plates can be made that consist of 3 letters followed by 4 numbers given the restriction that if the first letter is an ‘N’, then the second letter must be a ‘Y’? New York license plates can be made that consist of 3 letters followed by 4 numbers given the restrictions that (1) if the first letter is an ‘N’, then the second letter must be a ‘Y’ and (2) if the second letter is...

Subjects