Multiplication principle - practice problems - page 2 of 31
Examples:1. Outfit Selection:
- You have 3 shirts and 4 pants. How many different outfits can you make?
- Solution: 3 × 4 = 12 possible outfits.
2. Coin and Die Toss:
- How many outcomes are possible when tossing a coin (2 outcomes) and rolling a die (6 outcomes)?
- Solution: 2 × 6 = 12 possible outcomes.
3. Password Combinations:
- A password consists of 2 letters (A-Z, 26 options each) followed by 3 digits (0-9, 10 options each). How many passwords are possible?
- Solution: 26 × 26 × 10 × 10 × 10 = 262 × 103 = 676,!000 .
Number of problems found: 609
- Wooden
A wooden cube with an edge of 12 cm is painted with red paint. After the paint dries, the cube is cut into small cubes with an edge of 2 cm. Write how many small cubes will have exactly two red faces. - Flower - permutations
At a flower shop, there are 5 different kinds of flowers: tulips, lilies, daisies, carnations, and roses. There are also 3 different colours of vases: blue, green, and pink. If one kind of flower and one colour of vase are selected at random, what is the - At Junior's
A pizzeria offers pizza with tomato and cheese as a base. If a customer wishes, they may add toppings from the following options: ham, mushrooms, corn, and onion, each ingredient at most once. Every pizza is available in three sizes: small, medium, and la - A car license plate
A car licence plate consists of one letter (out of 26) and six digits. How many different plates can be formed if the letter is always in the second position and cannot be adjacent to a zero? - On the windowsill On the windowsill, 6 different flowers in flower pots are to be arranged next to each other. Four are flowering (one of them is a primrose), the rest are decorative with leaves (one of them is a fern). Determine: a) how many different arrangements can be
- Morse code 2
We have two characters: a dot and a comma. How many two-character and three-character sequences can be created using them, with repetition allowed? - 9 rectangles
A large rectangle is divided into 9 small rectangles. How many rectangles are there in total (of all sizes)? - Footballers 2
Footballers have jerseys numbered 7, 8, 9, 10, and 11. The coach wants to send them to attack: a) so that no two even-numbered jerseys are adjacent, b) so that no two odd-numbered jerseys are adjacent. How many options does he have in each case? - In the library
We have 8 different books in a library. In how many ways can they be arranged? In how many ways can they be arranged if 3 specific volumes must appear in a fixed given order? In how many ways can they be arranged if three specific volumes must appear cons - Three dice 2
What is the probability that exactly two of the three dice show the same odd number when three dice are rolled? - In class 24
There are a total of 16 students in the class, a quarter of whom are girls. A team of five is selected at random. Determine the probability that the team will have: a) at least 4 girls, b) at most 1 girl, c) no girls. - Christmas 4
There are only 3 packages left under the tree — two for Julia and one for Susan. Julia takes two at once. What is the probability that both packages belong to her? - 5D decimal How many five-digit numbers contain exactly 2 fours and exactly 3 sevens in their decimal notation?
- HAMMER 4
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word CAL. - Members 2
The members of a housing cooperative elected a seven-member board. In how many ways can a chairman, vice-chairman, treasurer, and secretary be chosen from among them? - Books in Slovak and English Vera has 4 Czech and 3 English books. She wants to arrange them on a shelf so that the Czech books come first and the English books second. In how many ways can this be done?
- Birthday boy 2
In how many ways can seven people be seated around a table if the birthday boy must sit at the head? - HAMMER 3
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word WATER. - Relay
A relay race will be run by the class team of Kate, Alice, Michaela, and Erica. Determine how many different running orders are possible, given that each of them can run in any position. - Beads
We have 4 beads: one green, one yellow, and 2 pink. In how many possible ways can we string them onto a string?
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