Answer:
Step-by-step explanation:
We are given that total number of bulbs are = 100.
Number of bulbs are tested = 3.
Please note, when order it not important, we apply combination.
Choosing 3 bulbs out of 100 don't need any specific order.
Therefore, applying combination formula for choosing 3 bulbs out of 100 bulbs.
[tex]^nCr = \frac{n!}{(n-r)!r!}[/tex] read as r out of n.
Plugging n=100 and r=3 in above formula, we get
[tex]^100C3 = \frac{100!}{(100-3)!3!}[/tex]
Expanding 100! upto 97!, we get
=[tex]\frac{100\times 99\times 98\times 97!}{97!3!}[/tex]
Crossing out common 97! from top and bottom, we get
=[tex]\frac{100\times 99\times 98}{3!}[/tex]
Expanding 3!, we get
=[tex]\frac{100\times 99\times 98}{3\times 2\times 1}[/tex]
= 100 × 33 × 49
= 161700 ways.
