Question

11. There are eleven seniors and five juniors who are sprinters on the high school track team. The coach must select four sprinters to run the 800-meter relay race.
a. How many 4-sprinter relay teams can be formed from the group of 16 sprinters?
b. In how many ways can two seniors be chosen to be part of the relay team?
c. In how many ways can two juniors be chosen to be part of the relay team?
d. In how many ways can two seniors and two juniors be chosen to be part of the relay team?
e. What is the probability that two seniors and two juniors will be chosen for the relay team?

Answer 1

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  = number of choices

r = number of person to be selected

number of ways = $^nC_r$

a) 4-sprinter relay teams can be formed from the group of 16 sprinters

n = 16

r = 4

= ¹⁶C₄

= $\frac{16!}{4!(16-4)!}$

= $\frac{16\times15\times14\times13\times12!}{4\times3\times2\times1(12!)}$

=

b)  two seniors be chosen to be part of the relay team

n = 11

r = 2

= ¹¹C₂

= $\frac{11!}{2!(11-2)!}$

= $\frac{11\times10\times9!}{2\times1(9!)}$

=

c)  two juniors be chosen to be part of the relay team

n = 5

r = 2

= ⁵C₂

= $\frac{5!}{2!(5-2)!}$

= $\frac{5\times4\times3!}{2\times1(3!)}$

= 10

d)  two seniors and two juniors be chosen to be part of the relay team

=  two seniors be chosen to be part of the relay team ×  two juniors be chosen to be part of the relay team

= 55 × 10

= 550

e) P( two seniors and two juniors will be chosen for the relay team )

= [  two seniors and two juniors be chosen to be part of the relay team ] ÷ [4-sprinter relay teams can be formed from the group of 16 sprinters ]

= 550 ÷ 1820

= 0.30219 ≈ 0.3022