Answer
a. $0.0003$
b. $0.089$
c. $0.053$
d. $0.496$
Work Step by Step
There are 65 players altogether.
Select 4 out of 65, we have $_{65}C_4$=677040
a. All 4 are seniors
Select 4 seniors out of 10, $_{10}C_4$=210, so $p=210/677040=0.0003$
b. There is 1 each: freshman, sophomore, junior, and senior
Choices $20\times20\times15\times10=60000$, $p=60000/677040=0.089$
c. There are 2 sophomores and 2 freshmen
Outcomes $_{20}C_2$*$_{20}C_2$=36100, $p=36100/677040=0.053$
d. At least 1 of the students is a senior
No seniors, $_{55}C_4$=341055, complement $p=1-341055/677040=0.496$
