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When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.(a) 17(b) 28(c) 11(d) 43I got this question in class test.My question is taken from Counting in division Counting of Discrete Mathematics

Answer»

The correct CHOICE is (c) 11

The explanation is: The question REQUIRES you to find number of the outcomes in which at most 2 coins TURN up as heads i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads. The number of outcomes in which 0 coins turn heads is ^4C0 = 1 outcome. The number of outcomes in which 1 coin turns head is ^4C1 = 6 outcomes. The number of outcomes in which 2 coins turn heads is,

^4C2 = 15 outcomes. Therefore, total number of outcomes = 1 + 4 + 6 = 11 outcomes.



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