Special license plates are made up of 2 letters followed by 4 digits. How many c

Question

Special license plates are made up of 2 letters followed by 4 digits. How many can be made: a) If all the letters are made of the same letter, while the digits can be any digit. b) If all the digits are made of the same digit, while the letters can be any letter. How many bit strings of length 8 can be made such that they begin with one zero and end with end with zero? Given a list of 5000, find out: a) How many persons are at least born on the same day of the week? b) How many persons are at least born on the same month? The following represents the sequence; 3, 4, 6, 8, 9 a) How many numbers must be selected if at least three of the selected numbers must add up to 18 b) How many numbers must be selected if at least two of the selected numbers must add up to more than 10

Explanation / Answer

1:

We assume that we have 26 letter and 0-9 digits

License plate can be written as L1L2D1D2D3D4

a:

Same letter and any digit

Eg AA1111 BB2242

Number of 4 digits

10 possible number

10 possible number

10 possible number

10 possible number

So total number of possible 4 digit: 10 x 10 x 10 x 10=10,000

So for each of 10000 we can 26 different letters.

So ans = 26* 10000=260000

b:

If all digits are made of same digit we only have 10 possible numbers

0000

1111

2222

3333

4444

5555

6666

7777

8888

9999

For each letter we have 26 options

So total possible combination of letter is 26*26=676

So each of possible combinations of letter we have 10 option for digits

So ans = 676*10=6,760

2: Bit string of length 8 and start and end with 0

0 fixed

0/1

0/1

0/1

0/1

0/1

0/1

0 fixed

So total possible bit strings are

1 x 2 x 2 x 2 x 2 x 2 x 2 x1 = 64

3:

a:

Here we can pigeon hole principle

There are 52 weeks and 5000 people

So there will be 52 same days i.e 52 Monday, Tuesday and so on

So there will be

5000/52=96.1538

So atleast 97 will be born on same day of week.

b:

Here we can pigeon hole principle

There are 12 months and 5000 people

So by pigeon hole principle

5000/12=416.6667

So atleast 417 people will be born on same month

Dear friend,

As per chegg policy we expert should answer 1 question or atmost 4 subquestions so that I am answering first 3 questions and its subquestions . Hope this helps you.

10 possible number

10 possible number

10 possible number

10 possible number

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