Question 1158083
At first, there is a total of {{{3+6+8=17}}} cards to draw from.
After the first card is drawn, there will be {{{17-1=16}}} cards to draw from.
After the first card and second have been drawn, there will be {{{17-2=15}}} cards to draw from.
 
(a) Probability that the questions are history, literature, and science, in that order:
 
At first,
{{{17}}} cards to draw from, including {{{3}}} history cards.
The probability that the first card drawn is a history card is
{{{3/17}}} .
After that,
{{{16}}} cards to draw the second card from, including all {{{6}}} literature cards.
The probability to draw a literature card after having drawn a history card is
{{{6/16=3/8}}} .
After that,
{{{15}}} cards to draw the third card from, including all {{{8}}} science cards. 
The probability to draw a science car after having drawn a history card followed by a literature car is
{{{(8/15)}}}

The probability that the questions are history, literature, and science, in that order is
{{{(3/17)(3/8)(8/15)=3*3*8/(17*8*15)=3/(17*5)=3/85=highlight(0.0353)}}} (rounded to four decimal places).

 
(b) Probability that all three cards drawn are literature questions:
 
At first,
{{{17}}} cards to draw from, including {{{6}}} literature cards.
The probability that the first card drawn is a literature card is
{{{6/17}}} .
After that,
{{{16}}} cards to draw the second card from, including {{{6-1=5}}} literature cards.
The probability to draw a second literature card after having drawn a literature card is
{{{5/16}}} .
After that,
{{{15}}} cards to draw the third card from, {{{6-2=4}}} literature cards. 
The probability to draw a third literature card after two literature cards is
{{{(4/15)}}}
 
The probability that all three questions drawn are literature questions is
{{{(6/17)(5/16)(4/15)=6*5*4/(17*16*15)=120/4080=highlight(0.0314)}}} (rounded to four decimal places).

 
(c) Probability that the first card drawn is science, the second is history, and the third is science
 
At first,
{{{17}}} cards to draw from, including {{{8}}} science cards.
The probability that the first card drawn is a science card is
{{{8/17}}} .
After that,
{{{16}}} cards to draw the second card from, including {{{3}}} history cards and {{{8-1=7}}} science cards.
The probability to draw a history card after having drawn a science card is
{{{3/16}}} .
After that,
{{{15}}} cards to draw the third card from, including {{{8-1=7}}} science cards. 
The probability to draw a science card after having drawn a science card and a history card is
{{{(7/15)}}}
 
The probability that the first card drawn is science, the second is history, and the third is science is
{{{(8/17)(3/16)(7/15)=8*3*7/(17*16*15)=168/4080=highlight(0.0412)}}} (rounded to four decimal places).