Question: A jewelry store chain with 5 stores in state A, 10 stores in state B, and 12 in state C is planning…

A jewelry store chain with 5 stores in state A, 10 stores in state B, and 12 in state C is planning to close 10 of these stores. Complete parts (A) and (B) below. … (A) How many ways can this be done? Determine the appropriate expression to evaluate. Select the correct choice and fill in the answer boxes to complete your choice. A. C B. P

Solution

A jewelry store chain has 5 stores in state A, 10 stores in state B, and 12 stores in state C, with plans to close 10 stores in total. We need to determine how many ways this can be done, so we need to use combinations as the order in which the stores are closed does not matter. First, we calculate the total number of stores: \[ 5 + 10 + 12 = 27 \] Next, we use the combination formula to select 10 stores to close out of 27: \[ \binom{27}{10} \] Therefore, the correct choice is: \[ \text{A. } \binom{27}{10} \]