Question

an environmental agency is analyzing soil samples from 50 farms for lead contamination. eight of the farms have dangerously high levels of lead. ten farms are randomly selected from the sample. using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?

Answer 1

Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.

Permutation and Combination

Combination is a mathematical way to arranging the set of values randomly.

ⁿCᵣ = n! / r! (n-r)!

we have given that ,

total number of farms for lead contamination = 50

Number of farms have dangerously high level of lead = 8

so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42

We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .

Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28

Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈

= 42! / 8! 34! = 42×41×---×35/8×7×----×1

= 118013185

The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .

= 118030185× 28 = 3,304,845,180

To learn more about Combination and Permutation, refer:

brainly.com/question/28065038

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