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mayaa2351
03.03.2020 •
Mathematics
Suppose that there are 15 antennas in a store, of which 3 are defective. Assume all the defectives and all the functional antennas are indistinguishable. If we lay all the antennas down in a row, how many linear orderings are there in which no two defectives are consecutive?
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Ответ:
Step-by-step explanation:
Total number of antenna is 15
Defective antenna is 3
The functional antenna is 15-3=12.
Now, if no two defectives are to be consecutive, then the spaces between the functional antennas must each contain at most one defective antenna.
So,
We line up the 13 good ones, and see where the bad one will fits in
__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __
Each of the places where there's a line is an available spot for one (and no more than one!) bad antenna.
Then,
There are 14 spot available for the defective and there are 3 defective, so the arrange will be combinational arrangement
ⁿCr= n!/(n-r)!r!
The number of arrangement is
14C3=14!/(14-3)!3!
14C3=14×13×12×11!/11!×3×2
14C3=14×13×12/6
14C3=364ways
Ответ:
P(x<10) =0
Step-by-step explanation:
M =1/μ
M= 1/15 =0.066667
X- Exp (0.066667)
Where: X is the random variable for number of days
P (X<x) = 1 - e^-mx
P(X - x) = 1 - e^-0.06666 x10
P(x<10) = 0