Cinema

How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?

Correct answer:

x =  4368

Step-by-step explanation:

$$\begin{gathered} C_{11}(16)=\left({\displaystyle \genfrac{}{}{0px}{}{16}{11}}\right)={\displaystyle \frac{16!}{11!(16-11)!}}={\displaystyle \frac{16\cdot 15\cdot 14\cdot 13\cdot 12}{5\cdot 4\cdot 3\cdot 2\cdot 1}}=4368 \\ n=6 \\ k=11 \\ x=\left(\genfrac{}{}{0px}{}{n+k-1}{k}\right)=\left(\genfrac{}{}{0px}{}{6+11-1}{11}\right)=4368 \end{gathered}$$

Try another example

Showing 4 comments:

Math student

wrong

3 years ago  Like

Math student

shouldn't it be 4368 ( 16 choose 11)

3 years ago  Like

Dr Math

are you sure? Aren't combinations with repetition?

3 years ago  Like

Math student

The answer is 4368. It’s a combination with repetition problem with n=6, r= 11.

2 years ago  Like

Related math problems and questions:

• Divide
  How many different ways can three people divide 7 pears and 5 apples?
• Combinations 6
  6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap, and 1 strap. How many are possible combinations?
• Candy
  How many ways can divide 10 identical candies to 5 children?
• Beads
  How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
• 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?
• 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?
• 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?
• Chocolates
  In the market we have 3 kinds of chocolates. How many ways can we buy 14 chocolates?
• Honored students
  Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?
• Combinations of sweaters
  I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
• 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?
• Lock
  A combination lock will open when the right choice of 3 numbers (from 1 to 16 inclusive) is selected. A. How many different lock combinations are possible? B. Is the combination lock named appropriately?
• Prize
  How many ways can be rewarded 9 participants with the first, second, and third prizes in a sports competition?
• Fruits
  In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?
• How many 13
  How many ways can X³ y⁴ z³ be written without an exponent?
• Five-digit numbers
  How many different five-digit numbers can be created from the numbers 2,3,5 if the number 2 appears in the number twice and the number 5 also twice?
• Math logic
  There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one wa