Aiko loves to have friends over for "Sushi night" where she rolls her own sushi based on her guests preferences. For tonight, she has 19 ingredients for her guests to choose from when creating their personal sushi roll recipe. How many possible different sushi roll recipes can Aiko make if she chooses 3 ingredients pr each roll?

Julian is arranging 162 chairs for a concert. He places the chairs in rows, with the same number of chairs in each row. Can he place the chairs in rows so that there are exactly 4 chairs per row? Why or why not?

The shape of the distribution of the time required to get an oil change at a 15​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 16.7 minutes​, and the standard deviation is 4.6 minutes. Complete parts​ (a) through​ (c) below.     ​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required?   Choose the required sample size below.     A. The sample size needs to be less than 30.   B. Any sample size could be used.   C. The sample size needs to be greater than 30. Your answer is correct.   D. The normal model cannot be used if the shape of the distribution is unknown. ​(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 15 ​minutes?   The probability is approximately 0.00660.0066. ​(Round to four decimal places as​ needed.) ​(c) Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a…

A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces. How many different recital programs are possible?