Respuesta :
Answer:
so there are 937433448 different ways to select polluted lake and 5 for non polluted lakes
Explanation:
we will use here fundamental counting principle
and formula for combination are
[tex]^n_c C = \frac{n!}{r! ( n - r ) !}[/tex] ...........................1
here n! = n ( n -1 ) . . . . . . . . . . . . . 3 . 2 . 1
so
here 78 lakes of which 6 are polluted so 78 - 6 = 72 are not polluted
so
we need select 1 of the 6 polluted
[tex]^6_1 C = \frac{6!}{1! ( 6 - r ) !}[/tex]
= [tex]\frac{6!}{1! * 5!} = \frac{6*5*4*3*2*1}{1*5*4*3*2*1}[/tex]
= 6
and
now we need to select 6 of 72 non polluted lakes
[tex]^{72}_6 C = \frac{72!}{6! ( 72 - 6 ) !}[/tex]
= [tex]\frac{72!}{6! * 66!}[/tex]
= 156,238,908
so
polluted lakes = 6 ways
ans non polluted lakes = 156,238,908 ways
so
fundamental counting principle
6 × 156,238,908 = 937433448
so there are 937433448 different ways to select polluted lake and 5 for non polluted lakes
Number of ways 1 polluted and 5 non-polluted lakes be chosen is 83,949,264
Permutation and combination:
Given that;
Number of lakes = 78
Number of lakes with high dioxin = 6
Find:
Number of ways 1 polluted and 5 non-polluted lakes be chosen
Computation:
Number of non-polluted lakes = 78 - 6
Number of non-polluted lakes = 72
Number of ways 1 polluted lake chosen = [tex]\frac{6!}{1!(6-1)!}[/tex]
Number of ways 1 polluted lake chosen = 6
Number of ways 5 non-polluted lake chosen = [tex]\frac{72!}{5!(72-5)!}[/tex]
Number of ways 5 non-polluted lake chosen = 13,991,544
Number of ways 1 polluted and 5 non-polluted lakes be chosen = 6 × 13,991,544
Number of ways 1 polluted and 5 non-polluted lakes be chosen = 83,949,264
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