Question

At the downtown office of First National Bank, there are three tellers. Last week, the tellers made the following numbers of errors: 4, 8, 3, 6, and 5. How many different samples of three tellers are possible

Answer 1

The number of different samples of three tellers possible is calculated using the combinations formula, resulting in 10 different samples. This applies combinatorics to determine all possible ways three tellers with given error counts can be selected.

Step-by-step explanation:

The student's question involves calculating the number of combinations of tellers possible given that there were three tellers and a set of errors they made last week: 4, 8, 3, 6, and 5. To solve this, we apply the concept of combinations from probability and combinatorics. The number of combinations of n items taken k at a time is given by the formula:

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

Here, we have a total of 5 errors (which we can think of as 'items') and we want to choose 3 of these (since there are 3 tellers). Plugging the values into the formula we get:

C(5, 3) = 5! / [3!(5-3)!] = (5*4*3*2*1) / [(3*2*1)*(2*1)] = (120) / [(6)*(2)] = 120 / 12 = 10.

Therefore, there are 10 different samples of three tellers possible given the errors they made last week.