Wagons

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 different trains can we assemble when:
The 1st train must have all six wagons
The 2nd train can have 1 to 6 wagons.

Correct result:

a =  90
b =  0

Solution:

$a={\displaystyle \frac{(2+2+2)!}{2!\cdot 2!\cdot 2!}}=90$

$b_{1}=1+1+1=3 \ \\ b=b_{2}=2+2+2=6=0$

Try another example

Showing 0 comments:

Next similar math problems:

• Combinations of sweaters
  I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
• Beads
  How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
• Three reds
  What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
• VCP equation
  Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
• Three-digit numbers
  How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
• 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?
• Roses 2
  Aunt Rose went to the flower shop to buy a bouquet with three roses. The flower shop had white, yellow and red roses. How many different flowers bouquet can a flower make for Aunt Rose create? Write all the bouquet options.
• Fruits
  In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?
• Chocolates
  In the market have 3 kinds of chocolates. How many ways can we buy 14 chocolates?
• Bouquets
  In the flower shop they sell roses, tulips and daffodils. How many different bouquets of 5 flowers can we made?
• 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?
• Flags
  How many different flags can be made from colors red, yellow, blue, green, white so that each flag consisted of three different colors?
• Eight blocks
  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
• Twelve flowers
  A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these 4 types of flowers would be possible?
• 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?
• Tricolors
  From the colors - red, blue, green, black and white, create all possible tricolors.
• Tokens
  In the non-transparent bags are red, white, yellow, blue tokens. We 3times pull one tokens and again returned it, write down all possibilities.