Question

The coach must select 12 players to travel to an away game. how many ways are there to select the players who will travel?

Answer 1

Answer with explanation:

Number of players who are selected for an away game =12

It is not given, that out of how many players we have to select 12 players.

If there are only 12 players, number of selecting 12 players

= 1 Way

If there are x players ,out of which we have to select 12 players

=As Order of selection is not important,so we will apply the rule of combinatorics here.

`_(12)^(x)\textrm{C}=(x!)/(12!* (x-12)!)`

Answer 2

The coach must select 12 players to travel to an away game. To find how many ways are there to select the players who will travel we use the combinations formula:
ⁿCr = n!/(n-r)!r!
Where,
n = 20
r = 12
Therefore,
₂₀C¹² = 20! / (20-12)!12!
₂₀C¹² = 20! / 8! 12!
₂₀C¹² = 20×19×18×17×16×15×14×13×12! / 8! 12!
₂₀C¹² = 20×19×18×17×16×15×14×13 / 8!
₂₀C¹² = 20×19×18×17×16×15×14×13 / 8×7×6×5×4×3×2×1
₂₀C¹² = 5,079,110,400/40,320
₂₀C¹² = 125,970

Hence, There are 125,970 ways to select the players who will travel.