Question 1006522
A warehouse employs {{{24}}} workers on first shift and {{{17}}} workers on second shift. 
Eight workers are chosen at random to be interviewed about the work environment. 

Using combinations, find the probability of choosing {{{6}}} first shift workers and {{{2}}} second shift workers.

Ways to pick {{{6}}} first and {{{2}}} second shift workers: 

{{{24C6*17C2}}}

{{{nCr=n!/(n-r)!(r!)}}}

{{{24C6=24!/(24-6)!(6!)}}}

{{{24C6=24!/(18)!(6!)}}}

{{{24C6=(24*23*22*21*20*19)/(6*5*4*3*2)}}}

{{{24C6=134596}}}



{{{17C2=17!/(17-2)!(2!)}}}

{{{17C2=17!/(15)!(2)}}}

{{{17C2=(17*16)/2}}}

{{{17C2=136}}}

Ways to pick {{{8}}} workers randomly: {{{41C8}}}

{{{41C8=41!/(41-8)!(8!)=95548245}}}

Answwer: {{{P(6 _first_ and_ 2_ second_shift) = (24C6*17C2)/41C8=(134596*136)/95548245 = 0.1916}}}