Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ How many different orders are there for obtaining 2 tails out of 4 coin flips?
a) 4
b) 6
c) 8
d) 12

To calculate the number of different orders for obtaining 2 tails from 4 coin flips, we use the combinations formula C(4, 2), which yields a result of 6. This indicates that there are 6 different ways to achieve this outcome. Correct option is b.

Explanation:

To determine the number of different orders for obtaining 2 tails out of 4 coin flips, we use combinatorics.

This type of question involves finding out the number of ways to select 2 tails (successes) from 4 flips (trials), which is a combination problem. Combinations do not take into account the order of the outcomes, which is perfect for this scenario since flipping a coin is an independent event.

The formula for calculating combinations is:

C(n, k) = n! / [k!(n-k)!]

Where 'n' is the total number of trials (4 coin flips) and 'k' is the total number of successful outcomes we're interested in (2 tails). Plugging in the numbers, we get:

C(4, 2) = 4! / [2!(4-2)!] = (4 × 3) / (2 × 1) = 6

So, the number of different orders to obtain 2 tails out of 4 coin flips is 6. This matches with option b) from the given choices.