Question

How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board positions. 3,003 120 360,360

Answer 1

3003 number of 5-member chess teams can be chosen from 15 interested players.

Explanation:

Given:

Number of the interested players = 15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula
`nCr = (n!)/(r!(n - r)!)`

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now we have n = 15 and r = 5

Substituting the values,

`15C_5 = (15!)/(5!(15- 5)!)`

`15C_5 = (15!)/(5!(10)!)`

`15C_5 = (15!)/(5!(10)!)`

`15C_5 = (15* * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 )/(5 * 4 * 3 * 2 * 1(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1))`

`15C_5 = (15* * 14 * 13 * 12 * 11)/((5 * 4 * 3 * 2 * 1))`

`15C_5 = (360360)/(120)`

`15C_5 = 3003`