A football team consists of 10 each freshmen and sophomores

A football team consists of 10 each freshmen and sophomores, 19 juniors, and 15 seniors. Four players are selected at random to serve as captains. Find the probability of the following. Use a graphing calculator and round the answer to six decimal places. Part 1 All 4 are seniors. P(4 seniors) = part 2 There are 1 each: freshman, sophomore, junior, and senior. P(1 of each) = Part 3 There are 2 sophomores and 2 freshmen. P(2 sophomores, 2 freshmen) = Part 4 At least 1 of the students is a senior. P( at least 1 of the students is a senior)

Solution

Total number= 10+10+19+15 =54

----------------------------------------------------------------------------------------------------------

(1) 15C4/54C4 = (15*14*13*12)/(54*53*52*51) =0.004316

----------------------------------------------------------------------------------------------------------

(2) 10*10*19*15/ 54C4

=28500/ ((54*53*52*51)/(1*2*3*4))

=0.090118

----------------------------------------------------------------------------------------------------------

(3)10C2*10C2/54C4

=(10*9/2) *(10*9/2)/ ((54*53*52*51)/(1*2*3*4))

=0.006403

----------------------------------------------------------------------------------------------------------

(4)P(at least 1 of the students is a senior)

=1-P(no of the students is a senior)

=1-39C4/54C4

=1- (39*38*37*36)/(54*53*52*51)

=0.739919