By James F. Adomanis
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Extra info for A Teacher's Guide to Colonial America: A History in Documents (Pages from History)
E drawn Am. (1",2, through n points no three of which are in the same line? , How many planes can be passed through 11 points, no 4 of them coplanar? 21. l;on has 17 vertices joined by lines. How many additional lines need to be drawn so that every pair of vertices will be Am. 119. connected? 22. A man has eight coins of different denominations. JIe pays out an amount of money consisting of not less than two nor more than six of the coins. How many diffe,rent amounts is it possible for him to payout with the given coins?
St one pair? , AM. all,&-"a~ •. & .... 1,281,072. (f) A. rds in the same suit. How many different flushes can be formed? ) , (g) A. rds of the same rank and a pair of another rank. How many different full houses are there (if a difference in suit only is to be counted as a different full house)? AM. 3,744. (h) A. ch. rds in each hand is unimportant but the order of the hands including the question as to which hand is given to the dealer is important. How many different deals are possible? 1l in the same suit.
The result above is used in ordinary experience in counting pairs of events. We state it then in the following form: FUNDAMENTAL COUNTING PRINCIPLE. 8econd event to take place in anyone of m waY8. Then the number oj waY8 in which the sequence oj two events can take place is nm. The result may be extended to triples of events, quadruples of events, etc. In every case the number of ways in which the sequence of events can occur is the product of the numbers of ways in which each entry can occur. job of counting depends upon what we are counting.
A Teacher's Guide to Colonial America: A History in Documents (Pages from History) by James F. Adomanis