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

By 161700 ways this test batch can be chosen.

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 = (n!)/((n-r)!r!)` read as r out of n.

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

`^100C3 = (100!)/((100-3)!3!)`

Expanding 100! upto 97!, we get

=
`(100* 99* 98* 97!)/(97!3!)`

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

=
`(100* 99* 98)/(3!)`

Expanding 3!, we get

=
`(100* 99* 98)/(3* 2* 1)`

= 100 × 33 × 49

= 161700 ways.

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