(a) Suppose that in a state, license plates have three letters followed by three

Question

(a) Suppose that in a state, license plates have three letters followed by three numbers, in a way that no letter or number is repeated in a single plate. Determine the number of possible license plates for this state. (b) A library has 800,000 books, and the librarian wants to encode by using a code word consisting of three letters followed by two numbers. Are there enough code words to encode all of these books with different code words? (a) In tossing four fair dice, what is probability of tossing, at most, one 4? (b) The elevator of a four-floor building leaves the first floor with six passengers and stops at all of the remaining three floors. If it is equally likely that a passenger gets off at any of these three floors, what is the probability that, at each stop of the elevator, at least one passenger departs? (a) Six fair dice are tossed. What is the probability that at least two of them show the same face? (b) Five boys and five girls sit at random in a row. What is the probability that the boys are together and the girls are together?

Explanation / Answer

4)a) 3 letter followed by 3 number

for letters- 26

for digits - 10

since without repition

26 ways for first letter , 25 for 2nd and 24 for 3rd one

similarly for digits

required number of ways = 26*25*24 *10*9*8 = 11232000

b) 3 letter and 2 number

number of permutation possible = 26^3 *10 ^2 = 1757600

since 1757600 > 800,000

there are enough codes

Please ask rest questions again,as per chegg polcy we have to answer 1 question only

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