College Math

College Math Study Guide

©2018 of 120 Hence, for the above example of 10 balls, out of which 6 are red and 4 are black, the total number of distinguishable permutations will become: 10! 6! 4! = (10∗9∗8∗7∗6!) 6!4! = 10*9*8*7/ 4*3*2*1 = 210 ways 4.5 Combinations In counting problems, it is not always necessary that order of drawing a set of r objects from a total of n objects is important. For instance, a player playing poker wants to know the total number of ways in which five cards can be drawn out of the deck of 52 cards, irrespective of the order of the cards being drawn. In such a case, we make use of combination. The rule for finding the number of combinations for drawing r objects from a set of n elements can be found by the following formula: ( , ) = ! ! ( − )! For the above instance of drawing five poker cards out of the deck of 52 cards, the possible combination will become: (52, 4) = 52! 4! ( 52 − 4)! = (52*51*50*49* 48!)/ (4!*48*) = 270725 ways It should be noted that the total number of combinations will be less than the total number of permutations. The different between permutations and combinations is the presence of order for permutations while there is an absence of order in combinations. 4.6 Probability Before we move on to understanding the meaning of probability, let us learn some basic terms which are used in probability. An experiment is a process that gives definite outcomes, like getting tails or heads on tossing a coin. As discussed before, a sample space provides the set of all the possible Achieve Page 67

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