Multiple choice

Six fair coins are tossed simultaneously. Number of ways in which atmost three of the coins turn up as heads in a definite order, is

  1. $32$
  2. $41$
  3. $42$
  4. $6$
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C Correct answer
Explanation

The number of ways to get at most 3 heads in 6 tosses is the sum of combinations: 6C0 + 6C1 + 6C2 + 6C3 = 1 + 6 + 15 + 20 = 42.

AI explanation

When six coins are tossed, finding the number of ways to get at most three heads means summing the combinations for getting exactly 0, 1, 2, and 3 heads. Using the combination formula, this sum is 6C0 + 6C1 + 6C2 + 6C3, equaling 1 + 6 + 15 + 20. Adding these values together yields a total of 42 ways.

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