10.) There were problems in the text about binary representation of numbers (onl

Question

10.) There were problems in the text about binary representation of numbers (only digits 0 and 1). For this problem, consider the quintary number system (only digits 0,1,2, 3 and 4).

a)How many different 6 digit numbers exist in the quintary number system?

b)How many different 6 digit numbers exist in the quintary number system ending in 0, 2 or 4?

c)How many different 6 digit numbers exist in the quintary number system end in 1 or 3?

d)How many different 6 digit numbers exist in the quintary number system have the first three digits only from the set {1, 2 or 3}?

e)How many different 6 digit numbers exist in the quintary number system have the first three digits being exactly 123?

f)Prove or disprove all quintary numbers ending in 0, 2 or 4 are equivalent to even integers in base 10?

11.) Given the letters of DISCRETEMATH, how many unique strings can be formed using all 12 letters?

Explanation / Answer

11. number of d =1

number of i =1

number of s =1

number of c =1

number of r =1

number of e =2

number of t =2

number of m =1

number of a =1

number of h =1

therefore total unique strings = 12 factorial/(2 factorial *2 factorial) =119750400

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