Question 1193319
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A company receives a shipment of 16 items. A random sample of 4 items is selected, 
and the shipment is rejected if any two of these items proves to be defective. 
What is the probability of accepting a shipment containing 4 defective items ?
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<pre>
The probability that the shipment will be  {{{highlight(highlight(accepted))}}}  is equal to the probability to find 0 or 1 
defective items in the random sub-set of 4 (four) items in the set of 16 items.


The number of all possible quadruples of 16 items is  {{{C[16]^4}}} = {{{(16*15*14*13)/(1*2*3*4)}}} = 1820.

The number of all possible quadruples of the form (0 defective,4 good) is  {{{C[4]^0*C[12]^4}}} = 1*495 = 495. 

The number of all possible quadruples of the form (1 defective,3 good) is  {{{C[4]^1*C[12]^3}}} = 4*220 = 880.

So the probability that the shipment will be accepted is

    P = {{{(495 + 880)/1820}}} = {{{1375/1820}}} = {{{275/364}}} = 0.755494505 = 75.55%  (rounded).    <U>ANSWER</U>
</pre>

Solved.