a) In Pascal's Triangle, which row has a sum of 33,554,432? b) Express as a single term in Pascal's Triangle in the form „C, 12C, + 12C5 . c) Explain what n and r represent in the expression nCr

Q: Find all possible digits that can be placed in the space so that the numbers is 1,182,1_4

A: Apply the rule for a number divisible by 9.

Q: Evaluate 10!/4!(10-4) Type an integer or a simplified fraction

A: It is needed to evaluated 10!/4!(10-4)!.

Q: 3) If every student in a class of 12 students gave a high-five to every other student, write an…

A: We have to find how many high-fives occurred in the class.

Q: Write the following (x: x-2, n is natural number less than 6) in roster form. (1, 2, 3, 4, 5}

A:

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: Determine the number of different words possible by rearranging the letters of ERRTDADX

A:

Q: Find the eighth row in Pascal's triangle. List the entries of the eighth row in Pascal's triangle in…

A: Solution-: We find the 8th row of pascal's triangle=?

Q: Subtract in binary. Place a 1 over each column from which it was necessary to borrow. (a)…

A: In binary system, 0-0=0 0-1=1  (borrow 1 as 0-1=-1<0) 1-0=1 1-1=0

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

A:

Q: Develop a divisibility test that will work for 45. Then prove your divisibility test for the…

A: The objective here is to develop a divisibility test of 45.A quick observation of the multiplication…

Q: How many different passwords exist that consist of 12 characte using uppercase and lowercase…

A:

Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

A:

Q: Prove that Leonardo's congruous numbers are always divisible by 24.

A:

Q: Is the number written correctly in scientific notation? Correct Scientific Notation Number 9) yes…

A: Since we know the scientific notation is m×10n, where m is the real number between 0 and 10. n is…

Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: If O is a natural number then O^2 + 2O + 1 is odd.

A: If O is a natural number then we need to check whether  O^2 + 2O + 1 is odd. The result is given…

Q: 28. What is the value being displayed by the abacus. I mot gaitisi2 moterye

A:

Q: What is the product using Pascal's triangle : (m-n)^3(m+n)^3

A:

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: Total ways to create a four digit passcodes of digits can be repeated

A: To find: The number of ways to create a four digit passcodes of digits. Calculation: The total…

Q: what are ALL the six-digit numbers of the form 47_8_6 that are divisible by 24?

A: The six-digit number has form 47__8__6

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many three-digit numbers can be formed by using the numerals in the set {1,2,4,5,6,7} if…

A: Hence,three-digit numbers can be formed by using the numerals in the set {1,2,4,5,6,7} if repetition…

Q: Show that 2 + V5 is irational number

A: