Question

If a coin is flipped 75 times, in how many ways could there be exactly two tails?

a. Subscript 73 Baseline P Subscript 2 Baseline = 5256
b. Subscript 73 Baseline C Subscript 2 Baseline = 2628
c. Subscript 75 Baseline C Subscript 2 Baseline = 2775
d. Subscript 75 Baseline P Subscript 2 Baseline = 5550

Answer 1

The number of ways to get exactly two tails when a coin is flipped 75 times is calculated using combinations, and the correct answer is option 'c' which represents 75C2 = 2775 ways.

Step-by-step explanation:

If a coin is flipped 75 times, the number of ways to get exactly two tails is calculated using combinations, as the order in which the tails appear does not matter. The relevant formula is the combination formula given by C(n, r) = n! / [(n-r)! r!], where n is the total number of items, and r is the number of items to choose.

Therefore, the correct calculation to find the number of ways to obtain exactly two tails in 75 coin flips would be 75C2, which calculates the combinations of 75 items taken 2 at a time.

This is equal to 75! / [(75-2)! 2!] = 75 * 74 / (2 * 1) = 2775 ways. Among the choices given, option 'c' represents the correct calculation: 75C2 = 2775.