Question

Use the following information to answer questions #2 and 3 The track team has 20 members and will be sending 5 members to the next competition. How many 5-person teams are possible?

Answer 1

the method is Combination

we have that

The formula for combinations is

C=n!/[(n-r)!*r!]

where

n is the total number of objects you choose from

r is the number that you choose to arrange

in this problem

n=20

r=5

substitute in the formula

C=20!/[(20-5)!*5!]

C=20!/[(15)!*5!]

C=(20*19*18*17*16*15!)/[15!*5!]

simplify

C=(20*19*18*17*16)/(5*4*3*2*1)

C=1,860,480/120

C=15,504