# Combinatorial number - math problems

#### Number of problems found: 139

• Binomial probability
What is the binominal probability that at least 4 of the 6 trials (n=6) are succeeded where φ = 0.50?
• C(6,3)
C(6,3) + 3 P(6,3)
• Committee 2
How many committee consisting of 3 women and 2 men can be formed from a group of 6 woman and 5 men?
• There 8
There are 7 women and 5 men in a department. a) how many ways can a committee of 3 people be selected? b) how many ways can a committee of 2 men and 1 woman be selected? c) how many ways can a committee of at least 2 woman be selected (3 people total)?
• Created trio
What is the probability that in the created trio, which consists of 19 boys and 12 girls, they will be: a) the boys themselves b) the girls themselves c) 2 boys and 1 girl?
• Bernoulli distribution
The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).
• The six
The six boys are to be led up the hill by a two-seater lift. How many options are there?
• Covid-19
Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• Doctors
The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
• Seeds
The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate?
• Wimbledon finals
Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus. If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
• Seedbeds
The father wants to plant 2 seedbeds of carrot and 2 seedbeds of onion. Use a tree chart to find how many different options for placing the seedbeds he has.
• Honored students
Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?
A license plate has 3 letters followed by 4 numbers. Repeats are not allowed for the letters, but they are for the numbers. If they are issued at random, what is the probability that the 3 letters are in alphabetical order and the 3 numbers are consecutiv
• School parliament
There are 18 boys and 14 girls in the class. In how many ways can 3 representatives be elected to the school parliament, if these are to be: a) the boys themselves b) one boy and two girls
• Two-element combinations
Write all two-element combinations from elements a, b, c, d.
• Soccer teams
Have to organize soccer teams. There are 3 age groups. How many different ways can you organize teams of ten for each age group? Is this a permutation or combination?
• Alopecia
Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most two men suffer from alopecia.
• Ten persons
Ten persons, each person makes a hand to each person. How many hands were given?
• Playing cards
From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red?

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