Question

a football team consists of 18 each freshman and sophemore 13 juniors and 15 seniors 4 players are selected at random to serve as captains find the probability of the following

all 4 are seniors

3 are seniors

2 are seniors

1 is senior

all 4 are juniors

Answer 1

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Given : There are 18 freshman and 19 sophomore, 15 seniors, 13 juniors.

a. P(all 4 are seniors)
= ways to select 4 from 15 seniors/ways to select 4 from 64 students
= 15C4/64C4
= 1365/635376
= 0.0021

b. P(3 are seniors, 1 any other)
= ways to select 3 from 15 seniors and 1 from any other/ways to select 4 from 64 students
= 15C3*49C1 / 64C4
= 276360/635376
= 0.0351

c. P(2 are seniors, 2 any other)
= ways to select 2 from 15 seniors and 2 from any other/ways to select 4 from 64 students
= 15C2*49C2 / 64C4
= 123480/635376
= 0.1943

d. P(1 senior, rest 3 from any other)
= ways to select 3 from 15 seniors and 1 from any other/ways to select 4 from 64 students
= 15C1*49C3 / 64C4
= 276360/635376
= 0.4350

e. P(all 4 are juniors)
= ways to select 4 from 13 juniors/ways to select 4 from 64 students
= 13C4 / 64C4
= 715/635376
= 0.0011