# math

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A manufacturer of light bulbs knows that 3% of the production of their 60W bulbs will be defective. What is the probability that exactly 5 bulbs in a carton of 144 will ne defective?
Did not understand the posted answer before, need it simplified.

• math -

One way for your problem could be

DDDDDGGG...GG , with 139 G's, where D stands for "defective" and is .03 and G stands for "good" and G is .97)

the prob of that particular case would be
(.03)^5 (.97)^139

but...
there are many ways to arrange DDDDDGGG...GG
There are 144 elements to arrange, 5 are alike of one kind, and 139 are alike of another.
The number of such ways = 144!/(5!139!)

That is how drwls got his answer of
(0.03)^5*(0.97)^139*144!/(139!*5!)

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