Question

A person tosses a coin 7 times. In how many ways can he get 5 heads?

Answer 1

Tossing a coin is a Binomial experiment. It consists some properties such as :

1.The experiment consists of n repeated trials

2. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.

3. The probability of success, denoted by p, is the same on every trial and failure is denoted by q such that p + q = 1 .

4. The trials are independent; that is, the outcome on on trial does not affect the outcome on other trials.

The two outcomes are head and tails.
Now, For 'n' repeated trials, the total number for k successes is given by ⁿC_k

Here n = 7, k = 5 .

there are ⁷C₅ = (7!) / (5! 2!) = 21 ways by which we can get 5 heads in 7 tosses of a coin.