Answer:
a) 17,100,720
b) 4,717,440
c) 10,920
d) 2821
Step-by-step explanation:
14 juniors and 16 seniors = 30 people
a) From the 30 members, how many ways are there to arrange 5 members of the club in a line?
As it is a ordered arrangement
30.29.28.27.26 = 17,100,720
b) How many ways are there to arrange 5 members of the club in a line if there must be a senior at the beginning of the line and at the end of the line?
16.28.27.26.15 = 4,717,440
c) If the club sends 2 juniors and 2 seniors to the tournament, how many possible groupings are there?
Not ordered arrangement. And means that we need to multiply the results.
C₁₄,₂ * C₁₆,₂
C₁₄,₂ = <u>14.13.12!</u> = <u>14.13 </u>= 91
12! 2! 2
C₁₆,₂ = <u>16.15.14!</u> = <u>16.15 </u>= 120
14! 2! 2
C₁₄,₂ * C₁₆,₂ = 91.120 = 10,920
d) If the club sends either 4 juniors or 4 seniors, how many possible groupings are there?
Or means that we need to sum the results.
C₁₄,₄ + C₁₆,₄
C₁₄,₄ = <u>14.13.12.11.10!</u> = <u>14.13.12.11 </u>= 1001
10! 4! 4.3.2.1
C₁₆,₄ = <u>16.15.14.13.12!</u> = <u>16.15.14.13 </u>= 1820
12! 4! 4.3.2.1
C₁₄,₄ + C₁₆,₄ = 1001 + 1820 = 2821
