11. There are eleven seniors and five juniors who are sprinters on the high school track team. The coach must select four sprint

Answer:

a) 1820

b) 55

c) 10

d) 550

e) 0.3022

Step-by-step explanation:

Data provided in the question:

Number of seniors = 11

Number of juniors = 5

n  = total options

r = persons to select

number of combinations =

a) The number of 4-sprinter relay teams from a total of 16 sprinters

n = 16

r = 4

= ¹⁶C₄

=

=

=

b)  The ways to select two seniors for the relay team

n = 11

r = 2

= ¹¹C₂

=

=

=

c)  The ways to choose two juniors for the relay team

n = 5

r = 2

= ⁵C₂

=

=

= 10

d)  The combination of two seniors and two juniors for the relay team

=  the number of ways to select two seniors ×  the number of ways to select two juniors

= 55 × 10

= 550

e) The probability that two seniors and two juniors are selected for the relay team

= [  the number of ways to select two seniors and juniors ] ÷ [the total number of possible 4-sprinter relay teams ]

= 550 ÷ 1820

= 0.30219 ≈ 0.3022