00:01
In this problem, it is said that a shipment of 102 laptops contain eight defective laptops.
00:06
A quality control specialist chooses a sample of nine laptops from this shipment.
00:11
Now, we need to answer a few questions based on this.
00:14
Now, first of all, we have been asked how many possible choices of nine laptops can be made.
00:19
So there are a total of 102 laptops, and we need to select any nine laptops at random from these 102 laptops.
00:26
This can be done in a hundred and two c -9 ways.
00:29
Here we use c which represents combination, and we use combination and not permutation in this case because the order of selection of the laptop does not matter.
00:38
Now, this is equal to 102 factorial by 9 factorial times a factorial of 102 minus 9, which is 93.
00:46
And if we calculate this, then this is equal to 2290 -415 -15 -15 -5.
01:01
780 .0.
01:03
So this is the required answer.
01:06
Next, we have been asked, how many of these selections will not contain any defective laptops? so there are 102 laptops out of which eight are defective.
01:15
So 102 minus 8, that's a total of 94 laptops which are not defective.
01:20
If we select any 9 out of them, then we will have a selection which contains no defective laptops.
01:25
This can be done in 94 c9 ways.
01:28
So we have 94 factorial by 9 factorial times a factorial of 94 minus 9, which is 85.
01:35
And if we calculate this, then this is equal to 106 -36 -72727575757 -57 -57 -57 -57 -55 -18...