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There are 26 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary? Answer:

There are 2626 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?\newlineAnswer:

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Full solution

Q. There are 2626 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?\newlineAnswer:
  1. Understand the problem: Understand the problem.\newlineWe need to find the number of different ways to choose 44 students from a group of 2626 for the positions of President, Vice President, Treasurer, and Secretary. Since the order in which we choose the students matters (because the positions are distinct), we will use permutations to solve this problem.
  2. Calculate the permutations: Calculate the number of permutations.\newlineThe number of ways to choose 44 students out of 2626 for distinct positions is given by the permutation formula, which is P(n,k)=n!(n−k)!P(n, k) = \frac{n!}{(n - k)!}, where nn is the total number of items to choose from, kk is the number of items to choose, n!n! denotes the factorial of nn, and (n−k)!(n - k)! is the factorial of (n−k)(n - k).\newlineIn this case, n=26n = 26 and 262600.
  3. Perform the calculation: Perform the calculation.\newlineP(26,4)=26!(26−4)!P(26, 4) = \frac{26!}{(26 - 4)!}\newline=26!22!= \frac{26!}{22!}\newline=26×25×24×23×22!22!= \frac{26 \times 25 \times 24 \times 23 \times 22!}{22!} (since the factorials cancel out)\newline=26×25×24×23= 26 \times 25 \times 24 \times 23\newline=358800= 358800

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