Question 1205739
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There are 27 marbles total, of which you are choosing 5.  The denominator of the probability fraction in every case is the total number of possible choices, which is C(27,5).<br>
The numerator of the probability fraction in each case is the number of ways of choosing the specified marbles.<br>
First question -- probability that all are red.  That means you choose 5 of the 10 red marbles and 0 of the other 17 marbles.  Note the "and" means you multiply the numbers of ways.<br>
ANSWER for the first problem: {{{(C(10,5)*C(17,0))/C(27,5)}}}<br>
For the other problems, you only need to change the expression in the numerator.  I'll let you do that; you won't learn anything from the problem if I do all the work for you.  You will probably want to use a calculator, as these numbers get rather large.<br>
Here is the calculation for a case different than in your post: find the probability that the 5 marbles are 1 red, 1 white, and 3 blue.  The calculation is<br>
{{{(C(10,1)*C(9,1)*C(8,3))/C(27,5)}}}<br>
As a check when setting up the calculation for any problem like this, note that the numbers in the numerator must match the numbers in the denominator.  In the preceding example, 10+9+8=27 and 1+1+3=5.<br>
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