Problem: A company is launching a new product, and they have conducted a survey to estimate the product's acceptance rate among potential customers. From the survey, they found that 70% of the respondents indicated that they would be likely to purchase the new product. The company decides to use this information to forecast sales and makes an initial batch of 20 products to test the market. Find the probability that a) exactly 10 customers will purchase the new product b) less than 5 customers will purchase the new product c) more than 12 customers will purchase the new product