Cups on the shelf

2 green, 3 red and 2 yellow cups should be placed side by side on the shelf.
a) How many different ways of setting up can arise?
b) How many different ways of arranging can arise if cups of the same color stand side by side?

Correct answer:

n =  210
b =  6

Step-by-step explanation:

n=7!2! 3! 2!=210
b=3 2 1=6



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




Tips to related online calculators
See also our permutations calculator.
See also our variations calculator.
Would you like to compute count of combinations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • Eight blocks
    cuboids Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
  • Wagons
    vlak2 We have six wagons, two white, two blue, and two red. We assemble trains from them, wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train, because I don't know any different. How many di
  • Numbers
    numbers How many different 3 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2?
  • Olympics
    olimpiada-medaliile In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
  • Flags
    vlajka_cz How many different flags can be made from colors red, yellow, blue, green, white to consist of three different colors?
  • Coffe cups
    hrnceky We have 4 cups with 4 different patterns. How many possible combinations can we create from 4 cups?
  • Shelf
    bookshelf How many ways are there to arrange 6 books on a shelf?
  • Combinations of sweaters
    sveter I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
  • Permutations with repetitions
    numbers2 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
  • Permutations
    permutations_3 How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: and, the digits must not be repeated in the number b, the number should be divisible by 5 and the numbers must not be repeated c, digits can be repeated
  • Beads
    koralky2 How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
  • School trip
    hostel The class has 19 students. What different ways can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number)
  • Divide
    hrusky How many different ways can three people divide 7 pears and 5 apples?
  • Pairs
    pair At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
  • Kids
    kids How many different ways can sit 8 boys and 3 girls in line if girls want to sit on the edge?
  • VCP equation
    combinatorics3 Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
  • Wedding guests
    svatba_hatalovi Fifteen wedding guests could not agree on who would stand in the wedding photo. The groom suggested that all possible sets of wedding guests be made in the photographs.