A blood bank needs 12 people to help with a blood drive. 19 people have volunteered. Find how many different groups of 12 can be formed from the 19 volunteers. Answer:

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Identify Concept: Identify the mathematical concept needed to solve the problem. To find the number of different groups of 12 that can be formed from 19 volunteers, we need to use the concept of combinations. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and ＂!＂ denotes factorial.Apply Formula: Apply the formula for combinations to the given numbers. We have 19 volunteers in total (n = 19) and we want to form groups of 12 (k = 12). So we need to calculate C(19, 12) = 19! / (12!(19-12)!).Simplify Expression: Simplify the expression by calculating the factorials and the division. C(19, 12) = 19! / (12! * 7!) = (19 * 18 * 17 * 16 * 15 * 14 * 13) / (7 * 6 * 5 * 4 * 3 * 2 * 1) since the factorials from 1 to 12 cancel out with part of the 19! factorial.Perform Calculations: Perform the calculations. C(19, 12) = (19 * 18 * 17 * 16 * 15 * 14 * 13) / (7 * 6 * 5 * 4 * 3 * 2 * 1) = 50388 / 5040 = 10

A blood bank needs $12$ people to help with a blood drive. $19$ people have volunteered. Find how many different groups of $12$ can be formed from the $19$ volunteers. $\newline$ Answer:

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