Mathematics, 23.07.2019 05:50 omar9844

Among the contestants in a competition are 38 women and 22 men. if 5 winners are randomly selected, what is the probability that they are all men

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There are two ways to solve this problem:

(1) The basic way:
Total number of contestants = 38 + 22 = 60 contestant
Probability that 1 winner is a man = 22/60
Probability that 2 winners are men = (22/60) * (21/59)
Probability that 3 winners are men = (22/60) * (21/59) * (20/58)
Probability that 4 winners are men = (22/60) * (21/59) * (20/58) * (19/57)
Probability that 5 winners are men = (22/60)*(21/59)*(20/58)*(19/57)*(18/56)
Doing the calculation, we will find that:
probability that 5 winners are men = 0.0048217

(2) The combination way:
Total number of contestants = 38 + 22 = 60
probability that 5 winners are men = C(22, 5) / C(60, 5)
where:
C(n, r) = n! / ((n - r)! * r!)
(The exclamation mark refers to the factorial)
Now, we will substitute:
C (22,5) = (22)! / ((22-5)!*(5)!) = 26334
C (60,5) = (60)! / ((60-5)!*(5)!) = 5461512
Substitute to get the probability as follows:
probability that 5 winners are men = C(22, 5) / C(60, 5)
= (26334) / (5461512)
= 0.0048217

Answer from: Quest

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation:

Answer from: Quest

Aline graph should be used

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Among the contestants in a competition are 38 women and 22 men. if 5 winners are randomly selected,...