Teams

How many ways can divide 16 players into two teams of 8 member?

Result

n =  12870

Solution:

$n=C_{{ 8}}(16) = \dbinom{ 16}{ 8} = \dfrac{ 16! }{ 8!(16-8)!} = \dfrac{ 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 } { 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } = 12870$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Following knowledge from mathematics are needed to solve this word math problem:

Would you like to compute count of combinations?

Next similar math problems:

1. Volleyball
8 girls wants to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of this girls may trainer to choose?
On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
3. Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
4. Fish tank
A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
5. Examination
The class is 21 students. How many ways can choose two to examination?
6. A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 que
7. Division
Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
8. Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
9. Blocks
There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
10. Trinity
How many different triads can be selected from the group 43 students?
11. Weekly service
In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
12. Cards
The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
13. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
14. Calculation of CN
Calculate: ?
15. Balls
The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
16. Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
17. Sequence
Write the first 7 members of an arithmetic sequence: a1=-3, d=6.