# 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 result:

p =  0.03 %

#### Solution:

$n_{1}=1 \ \\ n=8 \ \\ n(S)=3 \ \\ n(T)=1 \ \\ n(R)=1 \ \\ n(E)=2 \ \\ n(D)=1 \ \\ \ \\ n_{2}=\dfrac{ n! }{ n(S)! \cdot \ n(T)! \cdot \ n(R)! \cdot \ n(E)! \cdot \ n(D)! } \ \\ \ \\ n_{2}=\dfrac{ 8! }{ 3! \cdot \ 2! }=3360 \ \\ \ \\ p=100 \cdot \ \dfrac{ n_{1} }{ n_{2} }=100 \cdot \ \dfrac{ 1 }{ 3360 }=\dfrac{ 5 }{ 168 }=0.03 \%$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

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

Math student
why is n1 = 1?

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

Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Would you like to compute count of combinations?

## Next similar math problems:

• Word MATEMATIKA
How many words can be created from the word MATEMATIKA by changing the order of the letters, regardless of whether or not the words are meaningful?
• Two groups
The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?
• Families 2
There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.
• Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with each other?
• Cards
From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
• Classroom
Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys
• Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
• Salami
How many ways can we choose 5 pcs of salami if we have 6 types of salami for 10 pieces and one type for 4 pieces?
How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
• Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace and 2 in the third?
• Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
• Raffle
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?
• Sum or product
What is the probability that two dice fall will have the sum 7 or product 12?
• Combinations of sweaters
I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
• Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
• Three reds
What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?