# Combinatorics | Number Theory Answers

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Consider the simple problem of placing four coloured balls: red, blue, green and white in 15

boxes. What are the numbers of distinct ways in which the balls can be placed in these

boxes, if each box can hold only one ball? Also write the generalized formula of this

numerical result.

Coach Tab will select 3 girls and 3 boys for

the mix volleyball games. If he has 7 girls

and 8 boys on the pool, how many different

combinations can he have?

The six digits of my employee reference code at work are all different the first digit is one and the last one is eight when the coat is written as 32 digit numbers the middle number is a square number and is exactly halfway between the other two numbers what are the middle two digits of my employee reference code

Find the integer a such that a ≡ 08(mod23) and −22 ≤ a ≤ 0.

1.If and are positive integers greater than 1 and are divisible by b, what

is the last digit of nb? Explain.

If n and b are positive integers greater than 1 and n is divisible by b, what

is the last digit of nb? Explain.

1. If a, b, m, n are positive integers such that 1 < a < b < n and ma = nb.

Which is bigger, m or n? Explain.

(x+2)2 is a prime number

Use Polya’s four-step problem solving strategy to solve the following.

1. Consider the street map. Trisha wishes to walk directly from point A to point B. How many

different routes can she take if she wants to go past Starbucks on Third Avenue?

2. A true-false quiz contains five questions. In how many ways can a student answer the

questions if the student answers two of the questions with “false” and the other three with

“true”?

3. Two U.S. coins have a total value of 35¢. One of the coins is not a quarter. What are the two

coins?

4. If six people greet each other at a meeting by shaking hands with one another, how many

handshakes will take place?

Evaluate C74

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