STRESSED word

Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.

Result

p =  0.03 %

Solution:

n1=1 n2=8!3! 2!=3360  p=100 n1n2=100 13360=51680.0298=0.03%n_{ 1 } = 1 \ \\ n_{ 2 } = \dfrac{ 8! }{ 3! \cdot \ 2! } = 3360 \ \\ \ \\ p = 100 \cdot \ \dfrac{ n_{ 1 } }{ n_{ 2 } } = 100 \cdot \ \dfrac{ 1 }{ 3360 } = \dfrac{ 5 }{ 168 } \doteq 0.0298 = 0.03 \%



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 4 comments:
#
Help
where does 3! and 2! come from?

#
Dr Math
some characters are repeated: 3xS + 2xE; so there is no difference between first second and third S or 1st or 2nd E char.

#
Math student
How did you get 3360

#
Math student
dividing the factorials of 8!= 40,320 / 3!= 6 x 2!=2 so 40,320/12=3360
8!= 8x7x6x5x4x3x2x1= 40,320

avatar









Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
See also our combinations with repetition calculator.
Would you like to compute count of combinations?
See also our permutations calculator.
See also our variations calculator.

Next similar math problems:

  1. Cards
    cards_8 From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
  2. Cards
    cards_4 The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
  3. travel agency
    nevesta Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
  4. One green
    gulicky In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
  5. A pizza
    pizza_11 A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
  6. Calculation of CN
    color_combinations Calculate: ?
  7. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  8. Fish tank
    zebra_fish A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
  9. Trinity
    trojka How many different triads can be selected from the group 43 students?
  10. Three reds
    sedma What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
  11. Bulbs
    bulb The probability that the bulb can operate 4000 hours is 0.3. What is the probability that exactly one of eight bulbs can operate 4000 hours?
  12. Family
    family_32 94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
  13. Internet anywhere
    normal_d_4 In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
  14. Component fail
    matica There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because exactly one of the.
  15. Balls
    spheres_1 The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
  16. Probability of malaria
    malaria A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patien
  17. Genetic disease
    flu One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited