he thirty-member Science Club is choosing a seven-member committee to determine which compet tend next year. How many different possible committees can be chosen? a. quad872,640 b. quad593,775 c.) 2,035,800 d. 658,008 e. quad1,560,780 atics Level Test 1

Question

he thirty-member Science Club is choosing a seven-member committee to determine which compet tend next year. How many different possible committees can be chosen? a.  quad872,640 b.  quad593,775 c.)  2,035,800 d. 658,008 e.  quad1,560,780 atics Level Test 1

Bytelearn · Accepted Answer

Identify Problem Type: Identify the type of problem. We need to find the number of ways to choose a seven-member committee from a thirty-member club. This is a combination problem because the order in which we select the committee members does not matter.Use Combination Formula: Use the combination formula. The number of ways to choose k members from a group of n members is given by the combination formula nCk = n! / (k! * (n-k)!), where ! denotes factorial.Apply Formula to Problem: Apply the combination formula to the given problem. Here, n = 30 (total members) and k = 7 (members to choose). Calculate 30C7 = 30! / (7! * (30-7)!).Simplify Factorials: Simplify the factorials. Calculate 30! / (7! * 23!) by canceling out the common terms in the numerator and the denominator. 30! / (7! * 23!) = (30 * 29 * 28 * 27 * 26 * 25 * 24) / (7 * 6 * 5 * 4 * 3 * 2 * 1).Perform Calculations: Perform the calculations. Divide each term in the numerator by a corresponding term in the denominator to simplify the calculation: 30/6 = 5 29 is a prime number and cannot be simplified. 28/7 = 4 27/3 = 9 26 is a prime number and cannot be simplified. 25/5 = 5 24/4 = 6 Now multiply the simplified numbers together: 5 * 29 * 4 * 9 * 26 * 5 * 6 = 593,775.Check Answer Choices: Check the answer choices. The calculated number 593,775 matches one of the given answer choices, which is option b.

Full solution

More problems from Find terms of a geometric sequence

Related topics