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

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:

ⁿ Cr = 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.