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.

Correct answer:

p =  0.0298 %

Step-by-step explanation:

$$\begin{gathered} n_1=1 \\ n=8 \\ n(S)=3 \\ n(T)=1 \\ n(R)=1 \\ n(E)=2 \\ n(D)=1 \\ {n}_2={\displaystyle \frac{n!}{n(S)!\cdot n(T)!\cdot n(R)!\cdot n(E)!\cdot n(D)!}} \\ {n}_2={\displaystyle \frac{8!}{3!\cdot 2!}}=3360 \\ p=100\cdot {\displaystyle \frac{n_1}{n_2}}=100\cdot {\displaystyle \frac{1}{3360}}={\displaystyle \frac{5}{168}}=0.0298\mathrm{\%} \end{gathered}$$

Try another example

Showing 6 comments:

Help

where does 3! and 2! come from?

2 years ago  Like

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.

2 years ago  Like

Math student

How did you get 3360

2 years ago  Like

Math student

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

2 years ago  Like

Math student

why is n1 = 1?

1 year ago  Like

Matematik

n1 is the count of positive card (word DESSERTS) -> only one. n2 are the count of all combinations

1 year ago  Like

Related math problems and questions:

• Families 2
  Seven hundred twenty-nine families are having six children each. The probability of a girl is 1/3, and the probability of a boy is 2/3. Find the number of families having two girls and four boys.
• Divide
  How many different ways can three people divide 7 pears and 5 apples?
• Logik game
  Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numb
• Permutations with repetitions
  How many times the input of 1.2.2.3.3.3.4 can be permutated into 4 digits, 3 digits and 2 digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried permutation fo
• VCP equation
  Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
• Sum on dice
  We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
• Three digits number 2
  Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2.
• Median or middle
  The number of hours of television watched per day by a sample of 28 people is given below: 4, 1, 5, 5, 2, 5, 4, 4, 2, 3, 6, 8, 3, 5, 2, 0, 3, 5, 9, 4, 5, 2, 1, 3, 4, 7, 2, 9 What is the median value?
• Three reds
  What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
• Five letters
  How many ways can five letters be arranged?
• Combinations 6
  6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap, and 1 strap. How many are possible combinations?
• Two aces
  From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
• Simplify 3
  Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
• Phone numbers
  How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
• Dd 2-digit numbers
  Find all odd 2-digit natural numbers compiled from digits 1; 3; 4; 6; 8 if the digits are not repeated.
• Boats
  Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
• One dice
  Calculate the probability of a roll of one dice with the numbers 1, 2, 3, 4, 5, 6 on the walls. Write the results in a notebook in the shape of a fraction in the basic form: 2/3. a, The number 1 falls on the cube. b, The number 5 falls on the cube. c, An