Question

As part of quality-control program, 3 light bulbs from each bath of 100 are tested. In how many ways can this test batch be chosen?

Answer 1

Answer:

By 161700 ways this test batch can be chosen.

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.

$^nCr = \frac{n!}{(n-r)!r!}$ read as r out of n.

Plugging n=100 and r=3 in above formula, we get

$^100C3 = \frac{100!}{(100-3)!3!}$

Expanding 100! upto 97!, we get

=$\frac{100\times 99\times 98\times 97!}{97!3!}$

Crossing out common 97! from top and bottom, we get

=$\frac{100\times 99\times 98}{3!}$

Expanding 3!, we get

=$\frac{100\times 99\times 98}{3\times 2\times 1}$

= 100 × 33  × 49

= 161700 ways.

Therefore,  by 161700 ways this test batch can be chosen.