Multiplication principle - practice problems - page 6 of 31

Number of problems found: 609

Conditional probability
Suppose a batch contains ten items, of which four are defective. Two items are drawn at random from the batch, one after the other, without replacement. What is the probability that: I) Both are defective? Ii) Is the second item defective?
A committee
A committee of 6 is chosen from 8 men and 7 women. If a particular man must be included, find how many committees are possible.
Six segmants
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
Overbooking flight
A small regional carrier accepted 12 reservations for a particular flight with 11 seats. Seven reservations went to regular customers who would arrive for the flight. Each remaining passenger will arrive for the flight with a 49% chance, independently of
A bag 4
A bag contains 18 balls that differ only in colour: 11 are blue and 7 are red. Two balls are picked one after the other without replacement. Find the probability that both are: (i) blue, (ii) the same colour, (iii) different colours.
Four digit codes
Given the digits 0-7. If repetition is not allowed, how many four-digit codes greater than 2000 and divisible by 4 are possible?
In an
In an ABCD square, n interior points are chosen on each side. Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square.
Compartment ball options
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have?
Probability - dice
I roll six six-sided dice; what is the probability that exactly three threes will fall?
Menu choice
In a Jollibee, you have a menu choice of C1, C2, and C3. For dessert, you have a choice of ice cream and mango peach. How many different options do you have?
A bag 2
A bag contains seven green and eight red jellybeans. How many ways can five jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 4?
Three-digit number creation
From the number 5,4,0,7,8, create three-digit numbers, so they do not repeat and solve the problem by calculation.
Competition in the class
There are 10 students in the class, of which 8 are girls and two are boys. We want to select three for the competition. What is the probability that they will be: a) 2 girls and 1 boy b) 1 girl and 2 boys c) 3 girls d) 3 boys e) at least 2 girls
Four-digit number creation
How many four-digit numbers can we assemble from the digits 2, 6, 3, 5, 1, and 9 if the numerals in the number cannot be repeated?
Shirt short combinations
Dustin has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school?
Probability - dices
We roll six dice. What is the probability that: a) a six falls twice b) six falls four times
Card selection ways
How many ways do we know to select three cards from a deck of seven cards so that there are two red and one green between them?
PIN code probability
When entering the PIN code, we used the digits 2, 3, 4, 5, and 7 only once. What is the probability that someone will guess our PIN code on the first try?
Group placement ways
I have eight groups. How could they place first, second, and third?
Three-digit number creation
How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?

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