Question 1200086
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The wording of the problem most definitely does NOT say the 5 outcomes are 3 heads followed by 2 tails in that order....<br>
The number of possible outcomes on 5 flips of the coin is 2^5 = 32.<br>
The number of ways (different orders) of getting 3 heads and 2 tails is the number of different ways of arranging the letters HHHTT.  By a well-known counting principle, that number of ways is {{{(5!)/((3!)(2!))=120/12=10}}}.<br>
So the probability of getting 3 heads and 2 tails is 10/32 = 5/16.<br>
Note for problems involving flipping fair coins, a familiarity with Pascal's Triangle is helpful.  The 5th row of Pascal's Triangle is<br>
1 5 10 10 5 1<br>
Those numbers represent, respectively, the numbers of different ways of getting 5, 4, 3, 2, 1, or 0 heads.<br>