# Combinations and Permutations

COUNTING PERMUTATION COMBINATIONS

1. In a monthly test, the teacher decides that there will be three questions, one from each chapter I, II and III of the book. If there are 12 questions in chapter I, 10 in chapter II and 6 in chapter III. In how many ways can three questions be selected? Justify your answer.

2. Find the total number of ways of answering 5 objective type questions, each questions having 4 choices. Justify your answer.

3. How many three digit numbers can be formed without using the digits 0, 2, 3, 4, 5, 6?

4. How many two digit odd numbers can be formed using the digits 0, 2, 3, 4, 5, 6?

5. Find the number of distinct permutations that can be formed all the letters of each word:

a) RADAR

b) UNUSUAL

c) RECURSION

6. Find and justify the number of ways that a party of seven persons can arrange themselves

a) in a row of seven chairs

b) around a circular table.

7. In how many ways can four books of mathematics, three books of history, three books of chemistry, two books of sociology be arranged on a shelf so that all books of the same subject are together? Justify.

8. The local ice cream shop sells ten different flavors of ice cream. How many different two-scoop cones are there? (A cone with a vanilla scoop on top of a chocolate scoop is considered the same as a chocolate cone with a scoop on top of a vanilla scoop.)

9. How many base 10 numbers have 3 digits? How many three-digits numbers have no two consecutive digits equal? How many have at least one pair of consecutive digits equal?

10. By plugging in the formula for prove that .

11. A farmer buys 3 cows, 2 pigs and 4 hens from a man who has 6 cows, 5 pigs and 8 hens. How many choices does the former have? Justify your answer.

12. How many proper subsets of {1, 2, 3, 4, 5} contain the numbers 1 and 5? How many of them do not contain the number 2? Justify your answers.

13. Give a real-world example where combination applies. Give an instance of the problem and the interpretation of the result.

https://brainmass.com/math/recurrence-relation/combinations-permutations-622395

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COUNTING PERMUTATION COMBINATIONS

1. In a monthly test, the teacher decides that there will be three questions, one from each chapter I, II and III of the book. If there are 12 questions in chapter I, 10 in chapter II and 6 in chapter III. In how many ways can three questions be selected? Justify your answer.

Solution:

Number of ways = 12*10*6 = 720

Answer: 720 questions

2. Find the total number of ways of answering 5 objective type questions, each questions having 4 choices. Justify your answer.

Solution:

Total number of ways = 4*4*4*4*4 = 45 = 1024

Answer: 1024

3. How many three digit numbers can be formed without using the digits 0, 2, 3, 4, 5, 6?

Solution:

This means that we can only use 1, 7, 8 and 9.

Number of three digit numbers = 4*4* 4 = 64

Answer: 64

4. How many two digit odd numbers can be formed using the digits 0, 2, 3, 4, 5, 6?

Solution:

For first digit there will be 5 choices and second digit there will be only two ...

#### Solution Summary

This posting explains the concepts of combinations and permutations by illustrating the examples.