When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

Question

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

25
41
22
42
31

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-01T13:21:41+06:00

Answer: Option 4

The question requires you to find number of the outcomes in which at most 3 coins turn up as heads. i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads. The number of outcomes in which 0 coins turn heads is, 6C0 = 1 outcome. The number of outcomes in which 1 coin turns head is, 6C1 = 6 outcomes. The number of outcomes in which 2 coins turn heads is, 6C2 = 15 outcomes. The number of outcomes in which 3 coins turn heads is, 6C3 = 20 outcomes. Therefore, total number of outcomes = 1 + 6 + 15 + 20 = 42 outcomes.