Multiplication principle - practice problems - page 3 of 31
Applications:- Probability (counting sample spaces).
- Combinatorics (counting arrangements).
- Computer science (algorithm complexity, password security).
This principle is essential for solving problems where multiple decisions are made in sequence.
Number of problems found: 609
- 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 received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the end of the t - Green cards
We draw 4 cards from a deck of 32 cards. In how many ways can we draw: a) exactly 2 aces, b) exactly 3 green cards? - In the shipment
There are 40 products in a shipment, of which 4 are defective. In how many ways can 5 products be selected so that exactly 3 of them are non-defective? - Hockey - game
A hockey goalkeeper has a save success rate of 93.5%. What is the probability that he keeps a clean sheet in a match when facing 25 shots? What is the probability that he concedes at most 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 to choose a route from Lehota via Hradec to Buda and back, such that no road is used twice. - Target - shooting
A shooter hits the target with a probability of 78%. Determine the probability that, in a competition where 3 shots are fired in succession, he misses only the first shot. Round the result to two decimal places. - Customer 5
A customer decided to buy a Laura bed with a wooden slatted frame (available in 2 types) and an extra-firm mattress (available in 4 types) in one of three colours. Determine how many different combinations of the Laura bed with a wooden slatted frame and - Repeatition not allowed How many four-digit numbers can be formed from the digits 3, 5, 8, and 9 if no digit may be repeated?
- Grouping - combinatorics In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people.
- Probability - coin
When tossing a coin 4 times in a row, what is the probability that a sign will come up 3 times? - The Celebration
Five boys and five girls were nominated for a celebration at a local school. How many ways can the prom king, prom queen, and two other students be chosen from those nominated? (The king must be a boy, and the queen must be a girl) - A lottery In a lottery, a person chooses four different natural numbers at random from 1 to 10, and if these four numbers match the four numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? (Th
- Product 3DN How many three-digit numbers are there whose product of digits is 5?
- Train Set Markings
For shorter distances, small train sets are marked with three different letters from the company name run; how many small sets can be marked like this? - Playmakers + coach
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - Refrigerator, lemonades
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other? - Married pairs
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Probability - coloured balls The cube has 6 blue, 8 red, and 10 green balls. The player randomly draws 3 balls. Determine the probability that he draws balls of the same color.
- PIN probability number
The mobile PIN has 4 characters. What is the probability that the PIN contains the number 7 and ends with the number 5? - Cinema seating ways
How many different ways can Millie, Peter, Joseph, and Renata sit next to each other in a cinema if Millie always sits in seat 1 and Peter always sits in seat 4? List all possibilities.
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