COMBINATORIX Flashcards
A special plate number is made up of three letters of the English alphabet followed by two-digit numbers. How many plate numbers are possible if:
a. the letters and digits can be repeated in the same plate number?
b. the letters and digits cannot be repeated in the same plate number?
a. 1,757,600 possibilities
b. 1,404,000 possibilities
Selecting an outfit from 8 choices of shirt and 4 choices of pants.
32 ways
Answering a 5-item True or False test.
32 ways
Picking up 3 kinds of fruits from a choice of 9 kinds.
729 fruit combos
Choosing a PIN of 3 digits if repetition is allowed? If repetition is not allowed?
a. 1000 pins
b. 720 pins
Picking a name with 3 letters of the English Alphabet composed of 2 vowels and a consonant.
525 names
A freshman has 4 examinations to take and there are 10 examination periods available. How many possible arrangements are there of his examination schedule?
5,040 arrangements
A shelf will hold only even number books. Given that 11 different books are available, find the number of different arrangements that can be made to fill the shelf.
55,440 arrangements
For the Dempo concert, 6 items are proposed. Only 4 items will put up at the concert. How many permutations of 4 concert items are there?
360 permutations
In how many ways can 9 different books be arranged on a shelf? If
another two books are added, what is the total number of permutations?
a. 362,880 arrangements
a. 362,882 arrangements
Four students go for dinner and order a hamburger, a fish burger, a cheeseburger and a beef burger (one burger for each). When the waitress returns with the food, she forgets which student orders which item and simply places a burger before each students. In how many ways can the waitress do this?
24 ways
How many signals can be made by arranging 9 flags in a line if 4 are red, 3 are blue and 2 are white?
1,260 ways
Five red marbles, 2 white marbles and 3 blue marbles are arranged in a row. If the marbles of the same color are not distinguishable from each other, how many different arrangements are possible?
2,520 arrangements
Find the number of permutations from the word MINIMUM
420 ways
Find the number of permutations from the handle THEATHELIZABETHENA
…
In how many ways can 6 different trees be planted in a circle?
120 ways
On the buffet there are 7 different appetizers from which to choose. The appetizers are arranged on a revolving tray. How many ways can the appetizers be organized?
720 ways
How many ways can 8 beads be placed on a bracelet with no clasp?
5,040 ways
How many different 11-member football teams can be formed from a possible 20 players if any player can play any position?
167,960 ways
In how many ways can you get 2 aces and 4 queens from a deck of 52 cards?
6 ways
In how many ways can 10 objects be split into two groups containing 4 and 6 objects, respectively?
210 ways
In how many ways can a committee of 5 people be chosen from 9 people?
126 ways
How many different committees consisting of 8 people can be formed from 12 men and 9 women if equal numbers of men and women are to be chosen?
62,370 ways
From a list of 20 suggested books, Amy must choose 4 to make a report. How many possible combinations are there?
4,845 ways
In how many ways can 2 men, 4 women, 3 boys and 3 girls
be selected from 6 men, 8 women, 4 boys and 5 girls if:
a) no restrictions are imposed
b) a particular man and woman must be selected?
a. 42,000 ways
b. 1,920 ways
A mall has 5 gates, how many ways can you enter and exit the mall with a different gate.
20 ways
How many 2 digit numbers can be formed from the 4 integers: 1, 2, 3, 4
2.1 With repetition
2.2 Without repetition
2.1) 16 digits
2.2) 12 digits
If two dice are rolled, how many outcomes are there?
3.1 How many of these have a dot greater than 8?
3.2 How many of these have a dot less than 10?
3.0)
3.1) 10
3.2) 30
A science club need to elect a President, Vice President, and Treasurer. There are 30 members and each of them are eligible for any of these 3 positions. How many ways can any 3 members be elected for these positions?
24,360
The new licensed plate consists of 3 letters followed by 3 digits. How many different licensed plates can be made if:
a. The first letter is a vowel
b. The first and last digit is an odd number
a. 3,380,000
b. 4,394,000
