A blood bank needs 12 people to help with a blood drive. 18 people have volunteered. Find how many different groups of 12 can be formed from the 18 volunteers. Answer:

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Identify Problem Type: Identify the type of problem. We need to find the number of combinations of 18 people taken 12 at a time. This is a combinatorics problem involving combinations without repetition.Use Combination Formula: Use the combination formula. The number of ways to choose k people from a group of n people is given by the combination formula: C(n, k) = n! / (k!(n - k)!) where n! denotes the factorial of n, which is the product of all positive integers up to n.Apply Formula: Apply the formula to our problem. We have n = 18 volunteers and we want to choose k = 12 people. So we need to calculate: C(18, 12) = 18! / (12!(18 - 12)!)Simplify Expression: Simplify the expression. C(18, 12) = 18! / (12! * 6!) We can cancel out the common factorial terms by expanding the factorials partially: 18! = 18 * 17 * 16 * 15 * 14 * 13 * 12! Now we can cancel the 12! on the numerator and denominator. C(18, 12) = (18 * 17 * 16 * 15 * 14 * 13) / 6!Calculate Result: Calculate the result. 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720 Now we divide the product of the numbers in the numerator by 720: C(18, 12) = (18 * 17 * 16 * 15 * 14 * 13) / 720Perform Division: Perform the division. C(18, 12) = (18 * 17 * 16 * 15 * 14 * 13) / 720 C(18, 12) = (18/6) * (17/1) * (16/4) * (15/5) * (14/2) * (13/1) C(18, 12) = 3 * 17 * 4 * 3 * 7 * 13 C(18, 12) = 3 * 3 * 4 * 7 * 13 * 17 C(18, 12) = 9 * 4 * 7 * 13 * 17 C(18, 12) = 36 * 7 * 13 * 17 C(18, 12) = 252 * 13 * 17 C(18, 12) = 3276 * 17 C(18, 12) = 55692

A blood bank needs $12$ people to help with a blood drive. $18$ people have volunteered. Find how many different groups of $12$ can be formed from the $18$ volunteers. $\newline$ Answer:

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A blood bank needs $12$ people to help with a blood drive. $18$ people have volunteered. Find how many different groups of $12$ can be formed from the $18$ volunteers. $\newline$ Answer: