Combinatorics | Number Theory Answers

Prove:

The following methods are useful for divisibility by 11.

1. Get the difference of the sum of the digits in the odd places and the sum

of the digits in the even places. If the result is divisible by 11, then 11|N.

Prove that if 𝑎|𝑏 and 𝑏≠0, then |𝑎| ≤ |𝑏|.

Express as a fraction

1.5°23°

Determine the number of distinguishable permutations of the letters ELEMENT. *

A.140

B.340

C.640

D.840

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from

Prove or disprove: For all x ∈Z,if x mod11=5,then x 2 mod11=3.

Prove for all integers a and b, if a mod 8 = 5 and b mod 8 = 3 then ab mod 8 = 7.

In how many ways can five science books and six mathematics book can placed on a shelf if they must be placed alternately

Which of the options in this scenario are correct? A car dealership has 10 BMWs , 5 KIAs , and 15 AUDIs. The ratio 3:2 compares.