Respuesta :
Answer:
a) 66045
b) 91
c) 253
d) 23023
e) 0.349
Step-by-step explanation:
Number of juniors = 14
Number of seniors = 23
n = number of available choices
r = numbers of persons to be selected
a) n = 37
r = 4
number of ways to select a group of four students = ³⁷C₄
= [tex]\frac{37!}{4!(37-4)!}[/tex]
= [tex]\frac{37\times36\times35\times34\times33!}{4\times3\times2\times1(33!)}[/tex]
= 66045
b) n = 14
r = 2
number of ways to select exactly two juniors = ¹⁴C₂
= [tex]\frac{14!}{2!(14-2)!}[/tex]
= [tex]\frac{14\times13\times12!}{2\times1(12!)}[/tex]
= 91
c) n = 23
r = 2
number of ways to select exactly two seniors = ²³C₂
= [tex]\frac{23!}{2!(23-2)!}[/tex]
= [tex]\frac{23\times22\times21!}{2\times1(21!)}[/tex]
= 253
d) number of ways to send two juniors and two seniors
= number of ways to select exactly two juniors × number of ways to select exactly two seniors
= ¹⁴C₂ × ²³C₂
= 91 × 253
= 23023
e) P(two juniors and two seniors are selected to attend the conference )
= number of ways to send two juniors and two seniors ÷ [number of ways to select a group of four students]
= 23023 ÷ 66045
= 0.3486 ≈ 0.349
