Multiplication principle - practice problems - page 2 of 29
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: 579
- Morse code 2
We have two characters, a dot and a comma. How many two-element and how many three-element characters can be created with repetition? - 9 rectangles
A large rectangle is divided into 9 small rectangles. How many rectangles are there in total? - Footballers 2
Footballers have jerseys with numbers 7, 8, 9, 10, 11. The coach wants to send them to attack a) so that even jersey numbers are not next to each other b) so that odd jersey numbers are not next to each other. How many options does he have? - In the library
We have 8 different books in the library. How many ways can they be arranged? How many possibilities are there if 3 volumes are to be in a certain order? How many possibilities are there if three volumes are to be in a row independently in order? - Three dice 2
What is the probability that two odd numbers will be the same when three dice are rolled? - In class 24
There are a total of 16 students in the class, a quarter of whom are girls. We randomly select a team of five. 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 Julka and one for Zuzka. Julka took two at once. What is the probability that both belong to her? - How many 172
How many five-digit numbers are there that have exactly 2 fours and exactly 3 sevens in their notation? - HAMMER 4
Determine how many ways can the letters of the word HAMMER be rearranged so that in this rearrangement some group of consecutive letters 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 recorder be chosen from among them? - Books in Slovak and English Vlasta has 4 Czech and 3 English books. She wants to arrange them on a shelf so that Slovak books are first and then English books are second. How many ways are there to do this?
- Birthday boy 2
In how many ways can seven people be seated around a table so that the birthday boy sits at the head? - HAMMER 3
Determine how many ways it is possible to rearrange the letters of the word HAMMER so that in this rearrangement some group of consecutive letters forms the word WATER. - Relay
The relay race will be run for the class of Katka, Alice, Michaela, and Erika. Determine how many different orders there are in which the girls can run, as long as each of them can run in any position. - Beads
We have 4 beads. One is green, one is yellow, and 2 are pink. In how many possible ways can we string them on a string? - In a football
In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner of the match received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the - Green cards
We draw 4 cards from 32 cards. In how many ways can we draw a) exactly 2 aces, b) 3 green ones - In the shipment
There are 40 products in the shipment. Of these, 4 are defective. In how many ways can we select 5 products so that exactly 3 of them are good? - Hockey - game
A hockey goalkeeper has a save success rate of 93.5%. What is the probability that he will keep a clean sheet in a match when facing 25 shots? What is the probability that he will concede a maximum of 2 goals? - Ways
There are 3 different roads from Lehota to Hradec and 4 different roads from Hradec to Buda. Determine the number of ways in which it is possible to choose the route from Lehota via Hradec to Buda and back so that no road is used twice.
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