Answer to Question #257822 in Statistics and Probability for MONI

Question

Q_3: Counting Techniques (Multiplication Rule) = 2.5 (1) Researchers at a large training event are offered 5 sightseeing tours on each of 5 days. In how many ways can a person arrange to go on a sightseeing tour planned by this training event? (2a) For the picture shown below, find out in how many ways are possible for IMEI and Serial numbers for a cell phone? If lower case alphabets are also allowed, then how will that change the total ways for the Serial numbers? (2b) For the picture shown below, find out in how many ways are possible for Serial numbers on a US One Dollar Bill? If lower case alphabets are also allowed, then how will that change the total ways for the Serial numbers? (4) In a petrol consumption research, each of 4 sports vehicles is tested using 5 different brands of petrol at 5 test sites located in different locations of Karachi. If 3 drivers are used in the research, and test runs are made once under each distinct set of conditions, how many test runs are needed?

Answer 1

1)

$n=5^5=3125$ ways

4)

number of tests for 4 sports vehicles using 5 different brands of petrol:

$n_1=5^4=625$ tests

at 5 test sites:

$n_2=625\cdot 5=3125$ tests

if 3 drivers are used:

$n=3\cdot 3125=9375$ tests

2a)

IMEI: 15 digits

$n=10^{15}$ ways

Serial number: first 3 places are capital letters and the rest is 11 digits

$n=26^3\cdot 10^{11}$ ways

if lower case alphabets are also allowed:

$n=52^3\cdot 10^{11}$ ways

2b)

Serial number: capital letter, 8 digits, capital letter

$n=26^2\cdot10^8$ ways

if lower case alphabets are also allowed:

$n=52^2\cdot10^8$ ways