A serial number is formed by three letters followed by two digits. The letters a
ID: 3223576 • Letter: A
Question
A serial number is formed by three letters followed by two digits. The letters are chosen from the first 10 letters of the alphabet and the digits are chosen from the integers 1-9 (inclusive). If letters and digits cannot be repeated, then how many serial numbers are possible? If neither letters nor digits can be repeated, then how many serial numbers are possible? If letters and digits can be repeated and a serial number is generated at random, then what is the probability that the number does not contain the digit 6? If letters and digits can be repeated and a serial number is generated at random, then what is the probability that the number does not contain repeated letters?Explanation / Answer
Total letters = 10
total digits = 9
Total = 19
serial number formed by 3 letters and 2 digits
a) total serial numbers possible without repitation = 19*18*17*16*15 = 1395360
b) letters and digits can be repeated = 19*19*19*19*19 = 2476099
c) probability of a serial number not containing digit 6 if repitaions are allowed =
total serial numbers with repitation and without number 6 = 18*18*18*18*18 = 1889568
total digits with repitaion = 2476099
P = 1889568 / 2476099 = 0.76312
d) probability that the serial number does not contain repeated letters =
total serial numbers where letters are not repeated = 10C3 * 9 * 9 * 5! / 2! = 583200
P = 583200 / 2476099 = 0.2355
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.