Question 1203031
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In addition to the solution to the first problem from the other tutor, using nCr numbers, here are two other more elementary ways to solve that one.<br>
These alternative methods only work for relatively simple problems like this one; however, they are useful methods for many similar problems.<br>
(1) Pick the books one at a time and find the probability that the dictionary is NOT selected; then the probability that it IS selected is 1 minus that probability.<br>
P(not selected first) = 8/9
P(not selected first and not selected second) = (8/9)(7/8) = 7/9
P(not selected first and not selected second and not selected third) = (8/9)(7/8)(6/7) = 6/9 = 2/3<br>
P(IS selected first or second or third) = 1 - 2/3 = 1/3<br>
(2) Pick the books one at a time and find the probability that the dictionary is selected either first or second or third.<br>
P(picked first) = 1/9
P(not picked first; picked second) = (8/9)(1/8) = 1/9
P(not picked first or second; picked third) = (8/9)(7/8)(1/7) = 1/9<br>
P(picked first or second or third) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3<br>
Note solving your second problem by either of these methods would be very tedious because of the many different sequences in which the 2 novels and 1 book of poems could be selected.  The nCr method shown by the other tutor is far more efficient for this problem.<br>