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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.

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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) 43

I got this question in class test.

My question is taken from Counting in division Counting of Discrete Mathematics

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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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